---
OA_place: publisher
OA_type: gold
PlanS_conform: '1'
_id: '22247'
abstract:
- lang: eng
text: "A linearly ordered (LO) k-colouring of a hypergraph is a colouring of its
vertices with colours 1, …, k such that each edge contains a unique maximal colour.
Deciding whether an input hypergraph admits LO k-colouring with a fixed number
of colours is NP-complete (and in the special case of graphs, LO colouring coincides
with the usual graph colouring).\r\nHere, we investigate the complexity of approximating
the “linearly ordered chromatic number” of a hypergraph. We prove that the following
promise problem is NP-complete: Given a 3-uniform hypergraph, distinguish between
the case that it is LO 3-colourable, and the case that it is not even LO 4-colourable.
We prove this result by a combination of algebraic, topological, and combinatorial
methods, building on and extending a topological approach for studying approximate
graph colouring introduced by Krokhin, Opršal, Wrochna, and Živný (2023)."
acknowledgement: "This research was supported by the Charles University project PRIMUS/21/SCI/014,
by the Ministry of Education, Youth\r\nand Sports of the Czech Republic under the
project MSCAfellow5_MUNI (CZ.02.01.01/00/22_010/0003229), and by the\r\nAustrian
Science Fund (FWF project P31312-N35). This research was funded by UKRI EP/X024431/1
and by a Clarendon\r\nFund Scholarship. This project has received funding from the
European Union’s Horizon 2020 research and innovation\r\nprogramme under the Marie
Skłodowska-Curie Grant Agreement No 101034413.\r\n"
article_number: '10'
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: Marek
full_name: Filakovský, Marek
id: 3E8AF77E-F248-11E8-B48F-1D18A9856A87
last_name: Filakovský
- first_name: Tamio Vesa
full_name: Nakajima, Tamio Vesa
last_name: Nakajima
- first_name: Jakub
full_name: Opršal, Jakub
id: ec596741-c539-11ec-b829-c79322a91242
last_name: Opršal
orcid: 0000-0003-1245-3456
- first_name: Gianluca
full_name: Tasinato, Gianluca
id: 0433290C-AF8F-11E9-A4C7-F729E6697425
last_name: Tasinato
- first_name: Uli
full_name: Wagner, Uli
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
citation:
ama: Filakovský M, Nakajima TV, Opršal J, Tasinato G, Wagner U. Hardness of linearly
ordered 4-colouring of 3-colourable 3-uniform hypergraphs. ACM Transactions
on Computation Theory. 2026;18(2). doi:10.1145/3779121
apa: Filakovský, M., Nakajima, T. V., Opršal, J., Tasinato, G., & Wagner, U.
(2026). Hardness of linearly ordered 4-colouring of 3-colourable 3-uniform hypergraphs.
ACM Transactions on Computation Theory. Association for Computing Machinery.
https://doi.org/10.1145/3779121
chicago: Filakovský, Marek, Tamio Vesa Nakajima, Jakub Opršal, Gianluca Tasinato,
and Uli Wagner. “Hardness of Linearly Ordered 4-Colouring of 3-Colourable 3-Uniform
Hypergraphs.” ACM Transactions on Computation Theory. Association for Computing
Machinery, 2026. https://doi.org/10.1145/3779121.
ieee: M. Filakovský, T. V. Nakajima, J. Opršal, G. Tasinato, and U. Wagner, “Hardness
of linearly ordered 4-colouring of 3-colourable 3-uniform hypergraphs,” ACM
Transactions on Computation Theory, vol. 18, no. 2. Association for Computing
Machinery, 2026.
ista: Filakovský M, Nakajima TV, Opršal J, Tasinato G, Wagner U. 2026. Hardness
of linearly ordered 4-colouring of 3-colourable 3-uniform hypergraphs. ACM Transactions
on Computation Theory. 18(2), 10.
mla: Filakovský, Marek, et al. “Hardness of Linearly Ordered 4-Colouring of 3-Colourable
3-Uniform Hypergraphs.” ACM Transactions on Computation Theory, vol. 18,
no. 2, 10, Association for Computing Machinery, 2026, doi:10.1145/3779121.
short: M. Filakovský, T.V. Nakajima, J. Opršal, G. Tasinato, U. Wagner, ACM Transactions
on Computation Theory 18 (2026).
corr_author: '1'
das_tickbox: '0'
date_created: 2026-07-05T22:01:37Z
date_published: 2026-05-04T00:00:00Z
date_updated: 2026-07-06T09:06:29Z
day: '04'
ddc:
- '500'
department:
- _id: UlWa
doi: 10.1145/3779121
ec_funded: 1
external_id:
arxiv:
- '2312.12981'
file:
- access_level: open_access
checksum: 0399ab94085878fc810084845eabd627
content_type: application/pdf
creator: dernst
date_created: 2026-07-06T09:03:02Z
date_updated: 2026-07-06T09:03:02Z
file_id: '22252'
file_name: 2026_TransactionsGraphics_Filakovsky.pdf
file_size: 941518
relation: main_file
success: 1
file_date_updated: 2026-07-06T09:03:02Z
has_accepted_license: '1'
intvolume: ' 18'
issue: '2'
keyword:
- Constraint satisfaction problem
- hypergraph colouring
- promise problem
- topological methods
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
project:
- _id: 26611F5C-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P31312
name: Algorithms for Embeddings and Homotopy Theory
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
call_identifier: H2020
grant_number: '101034413'
name: 'IST-BRIDGE: International postdoctoral program'
publication: ACM Transactions on Computation Theory
publication_identifier:
eissn:
- 1942-3462
issn:
- 1942-3454
publication_status: published
publisher: Association for Computing Machinery
quality_controlled: '1'
related_material:
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scopus_import: '1'
status: public
supplementarymaterial: no
title: Hardness of linearly ordered 4-colouring of 3-colourable 3-uniform hypergraphs
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 18
year: '2026'
...
---
OA_place: publisher
OA_type: hybrid
_id: '20008'
abstract:
- lang: eng
text: 'We study the complexity of a class of promise graph homomorphism problems.
For a fixed graph H, the H-colouring problem is to decide whether a given graph
has a homomorphism to H. By a result of Hell and Nešetřil, this problem is NP-hard
for any non-bipartite loop-less graph H. Brakensiek and Guruswami [SODA 2018]
conjectured the hardness extends to promise graph homomorphism problems as follows:
fix a pair of non-bipartite loop-less graphs G, H such that there is a homomorphism
from G to H, it is NP-hard to distinguish between graphs that are G-colourable
and those that are not H-colourable. We confirm this conjecture in the cases when
both G and H are 4-colourable. This is a common generalisation of previous results
of Khanna, Linial, and Safra [Comb. 20(3): 393-415 (2000)] and of Krokhin and
Opršal [FOCS 2019]. The result is obtained by combining the algebraic approach
to promise constraint satisfaction with methods of topological combinatorics and
equivariant obstruction theory.'
acknowledgement: This research was supported by the Austrian Science Fund (FWF project
P31312-N35) and by project MSCAfellow5_MUNI (CZ.02.01.01/00/22_010/0003229) financed
by the Ministry of Education, Youth and Sports of the Czech Republic. This project
has also received funding from the European Union’s Horizon 2020 research and innovation
programme under the Marie Skłodowska-Curie Grant Agreement No 101034413.
article_processing_charge: Yes (in subscription journal)
author:
- first_name: Sergey
full_name: Avvakumov, Sergey
id: 3827DAC8-F248-11E8-B48F-1D18A9856A87
last_name: Avvakumov
orcid: 0000-0002-7840-5062
- first_name: Marek
full_name: Filakovský, Marek
id: 3E8AF77E-F248-11E8-B48F-1D18A9856A87
last_name: Filakovský
- first_name: Jakub
full_name: Opršal, Jakub
id: ec596741-c539-11ec-b829-c79322a91242
last_name: Opršal
orcid: 0000-0003-1245-3456
- first_name: Gianluca
full_name: Tasinato, Gianluca
id: 0433290C-AF8F-11E9-A4C7-F729E6697425
last_name: Tasinato
- first_name: Uli
full_name: Wagner, Uli
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
citation:
ama: 'Avvakumov S, Filakovský M, Opršal J, Tasinato G, Wagner U. Hardness of 4-colouring
G-colourable graphs. In: Proceedings of the 57th Annual ACM Symposium on Theory
of Computing. Association for Computing Machinery; 2025:72-83. doi:10.1145/3717823.3718154'
apa: 'Avvakumov, S., Filakovský, M., Opršal, J., Tasinato, G., & Wagner, U.
(2025). Hardness of 4-colouring G-colourable graphs. In Proceedings of the
57th Annual ACM Symposium on Theory of Computing (pp. 72–83). Prague, Czechia:
Association for Computing Machinery. https://doi.org/10.1145/3717823.3718154'
chicago: Avvakumov, Sergey, Marek Filakovský, Jakub Opršal, Gianluca Tasinato, and
Uli Wagner. “Hardness of 4-Colouring G-Colourable Graphs.” In Proceedings of
the 57th Annual ACM Symposium on Theory of Computing, 72–83. Association for
Computing Machinery, 2025. https://doi.org/10.1145/3717823.3718154.
ieee: S. Avvakumov, M. Filakovský, J. Opršal, G. Tasinato, and U. Wagner, “Hardness
of 4-colouring G-colourable graphs,” in Proceedings of the 57th Annual ACM
Symposium on Theory of Computing, Prague, Czechia, 2025, pp. 72–83.
ista: 'Avvakumov S, Filakovský M, Opršal J, Tasinato G, Wagner U. 2025. Hardness
of 4-colouring G-colourable graphs. Proceedings of the 57th Annual ACM Symposium
on Theory of Computing. STOC: Symposium on Theory of Computing, 72–83.'
mla: Avvakumov, Sergey, et al. “Hardness of 4-Colouring G-Colourable Graphs.” Proceedings
of the 57th Annual ACM Symposium on Theory of Computing, Association for Computing
Machinery, 2025, pp. 72–83, doi:10.1145/3717823.3718154.
short: S. Avvakumov, M. Filakovský, J. Opršal, G. Tasinato, U. Wagner, in:, Proceedings
of the 57th Annual ACM Symposium on Theory of Computing, Association for Computing
Machinery, 2025, pp. 72–83.
conference:
end_date: 2025-06-27
location: Prague, Czechia
name: 'STOC: Symposium on Theory of Computing'
start_date: 2025-06-23
corr_author: '1'
date_created: 2025-07-13T22:01:23Z
date_published: 2025-06-15T00:00:00Z
date_updated: 2026-07-29T13:13:17Z
day: '15'
ddc:
- '000'
department:
- _id: UlWa
doi: 10.1145/3717823.3718154
ec_funded: 1
file:
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checksum: 2c9ae7ad0102c41124976f4cb5182760
content_type: application/pdf
creator: dernst
date_created: 2025-07-14T06:42:58Z
date_updated: 2025-07-14T06:42:58Z
file_id: '20013'
file_name: 2025_STOC_Avvakumov.pdf
file_size: 940827
relation: main_file
success: 1
file_date_updated: 2025-07-14T06:42:58Z
has_accepted_license: '1'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 72-83
project:
- _id: 26611F5C-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P31312
name: Algorithms for Embeddings and Homotopy Theory
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
call_identifier: H2020
grant_number: '101034413'
name: 'IST-BRIDGE: International postdoctoral program'
publication: Proceedings of the 57th Annual ACM Symposium on Theory of Computing
publication_identifier:
isbn:
- '9798400715105'
issn:
- 0737-8017
publication_status: published
publisher: Association for Computing Machinery
quality_controlled: '1'
related_material:
record:
- id: '20339'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Hardness of 4-colouring G-colourable graphs
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2025'
...
---
_id: '15168'
abstract:
- lang: eng
text: 'A linearly ordered (LO) k-colouring of a hypergraph is a colouring of its
vertices with colours 1, … , k such that each edge contains a unique maximal colour.
Deciding whether an input hypergraph admits LO k-colouring with a fixed number
of colours is NP-complete (and in the special case of graphs, LO colouring coincides
with the usual graph colouring). Here, we investigate the complexity of approximating
the "linearly ordered chromatic number" of a hypergraph. We prove that the following
promise problem is NP-complete: Given a 3-uniform hypergraph, distinguish between
the case that it is LO 3-colourable, and the case that it is not even LO 4-colourable.
We prove this result by a combination of algebraic, topological, and combinatorial
methods, building on and extending a topological approach for studying approximate
graph colouring introduced by Krokhin, Opršal, Wrochna, and Živný (2023).'
acknowledgement: "Marek Filakovský: This research was supported by Charles University
(project PRIMUS/\r\n21/SCI/014), the Austrian Science Fund (FWF project P31312-N35),
and MSCAfellow5_MUNI\r\n(CZ.02.01.01/00/22_010/0003229). Tamio-Vesa Nakajima: This
research was funded by UKRI EP/X024431/1 and by a Clarendon Fund Scholarship. All
data is provided in full in the results section of this paper. Jakub Opršal: This
project has received funding from the European Union’s Horizon 2020 research and
innovation programme under the Marie Skłodowska-Curie Grant Agreement No 101034413.
Uli Wagner: This research was supported by the Austrian Science Fund (FWF project
P31312-N35)."
alternative_title:
- LIPIcs
article_number: '34'
article_processing_charge: No
arxiv: 1
author:
- first_name: Marek
full_name: Filakovský, Marek
id: 3E8AF77E-F248-11E8-B48F-1D18A9856A87
last_name: Filakovský
- first_name: Tamio Vesa
full_name: Nakajima, Tamio Vesa
last_name: Nakajima
- first_name: Jakub
full_name: Opršal, Jakub
id: ec596741-c539-11ec-b829-c79322a91242
last_name: Opršal
orcid: 0000-0003-1245-3456
- first_name: Gianluca
full_name: Tasinato, Gianluca
id: 0433290C-AF8F-11E9-A4C7-F729E6697425
last_name: Tasinato
- first_name: Uli
full_name: Wagner, Uli
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
citation:
ama: 'Filakovský M, Nakajima TV, Opršal J, Tasinato G, Wagner U. Hardness of linearly
ordered 4-colouring of 3-colourable 3-uniform hypergraphs. In: 41st International
Symposium on Theoretical Aspects of Computer Science. Vol 289. Schloss Dagstuhl
- Leibniz-Zentrum für Informatik; 2024. doi:10.4230/LIPIcs.STACS.2024.34'
apa: 'Filakovský, M., Nakajima, T. V., Opršal, J., Tasinato, G., & Wagner, U.
(2024). Hardness of linearly ordered 4-colouring of 3-colourable 3-uniform hypergraphs.
In 41st International Symposium on Theoretical Aspects of Computer Science
(Vol. 289). Clermont-Ferrand, France: Schloss Dagstuhl - Leibniz-Zentrum für Informatik.
https://doi.org/10.4230/LIPIcs.STACS.2024.34'
chicago: Filakovský, Marek, Tamio Vesa Nakajima, Jakub Opršal, Gianluca Tasinato,
and Uli Wagner. “Hardness of Linearly Ordered 4-Colouring of 3-Colourable 3-Uniform
Hypergraphs.” In 41st International Symposium on Theoretical Aspects of Computer
Science, Vol. 289. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.
https://doi.org/10.4230/LIPIcs.STACS.2024.34.
ieee: M. Filakovský, T. V. Nakajima, J. Opršal, G. Tasinato, and U. Wagner, “Hardness
of linearly ordered 4-colouring of 3-colourable 3-uniform hypergraphs,” in 41st
International Symposium on Theoretical Aspects of Computer Science, Clermont-Ferrand,
France, 2024, vol. 289.
ista: 'Filakovský M, Nakajima TV, Opršal J, Tasinato G, Wagner U. 2024. Hardness
of linearly ordered 4-colouring of 3-colourable 3-uniform hypergraphs. 41st International
Symposium on Theoretical Aspects of Computer Science. STACS: Symposium on Theoretical
Aspects of Computer Science, LIPIcs, vol. 289, 34.'
mla: Filakovský, Marek, et al. “Hardness of Linearly Ordered 4-Colouring of 3-Colourable
3-Uniform Hypergraphs.” 41st International Symposium on Theoretical Aspects
of Computer Science, vol. 289, 34, Schloss Dagstuhl - Leibniz-Zentrum für
Informatik, 2024, doi:10.4230/LIPIcs.STACS.2024.34.
short: M. Filakovský, T.V. Nakajima, J. Opršal, G. Tasinato, U. Wagner, in:, 41st
International Symposium on Theoretical Aspects of Computer Science, Schloss Dagstuhl
- Leibniz-Zentrum für Informatik, 2024.
conference:
end_date: 2024-03-14
location: Clermont-Ferrand, France
name: 'STACS: Symposium on Theoretical Aspects of Computer Science'
start_date: 2024-03-12
corr_author: '1'
date_created: 2024-03-24T23:00:59Z
date_published: 2024-03-01T00:00:00Z
date_updated: 2026-07-29T13:13:17Z
day: '01'
ddc:
- '510'
department:
- _id: UlWa
doi: 10.4230/LIPIcs.STACS.2024.34
ec_funded: 1
external_id:
arxiv:
- '2312.12981'
isi:
- '001300393400034'
file:
- access_level: open_access
checksum: 0524d4189fd1ed08989546511343edf3
content_type: application/pdf
creator: dernst
date_created: 2024-03-25T07:44:30Z
date_updated: 2024-03-25T07:44:30Z
file_id: '15175'
file_name: 2024_LIPICs_Filakovsky.pdf
file_size: 927290
relation: main_file
success: 1
file_date_updated: 2024-03-25T07:44:30Z
has_accepted_license: '1'
intvolume: ' 289'
isi: 1
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
project:
- _id: 26611F5C-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P31312
name: Algorithms for Embeddings and Homotopy Theory
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
call_identifier: H2020
grant_number: '101034413'
name: 'IST-BRIDGE: International postdoctoral program'
publication: 41st International Symposium on Theoretical Aspects of Computer Science
publication_identifier:
eissn:
- 1868-8969
isbn:
- '9783959773119'
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
related_material:
record:
- id: '22247'
relation: later_version
status: public
- id: '20339'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Hardness of linearly ordered 4-colouring of 3-colourable 3-uniform hypergraphs
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 289
year: '2024'
...
---
_id: '10220'
abstract:
- lang: eng
text: "We study conditions under which a finite simplicial complex K can be mapped
to ℝd without higher-multiplicity intersections. An almost r-embedding is a map
f: K → ℝd such that the images of any r pairwise disjoint simplices of K do not
have a common point. We show that if r is not a prime power and d ≥ 2r + 1, then
there is a counterexample to the topological Tverberg conjecture, i.e., there
is an almost r-embedding of the (d +1)(r − 1)-simplex in ℝd. This improves on
previous constructions of counterexamples (for d ≥ 3r) based on a series of papers
by M. Özaydin, M. Gromov, P. Blagojević, F. Frick, G. Ziegler, and the second
and fourth present authors.\r\n\r\nThe counterexamples are obtained by proving
the following algebraic criterion in codimension 2: If r ≥ 3 and if K is a finite
2(r − 1)-complex, then there exists an almost r-embedding K → ℝ2r if and only
if there exists a general position PL map f: K → ℝ2r such that the algebraic intersection
number of the f-images of any r pairwise disjoint simplices of K is zero. This
result can be restated in terms of a cohomological obstruction and extends an
analogous codimension 3 criterion by the second and fourth authors. As another
application, we classify ornaments f: S3 ⊔ S3 ⊔ S3 → ℝ5 up to ornament concordance.\r\n\r\nIt
follows from work of M. Freedman, V. Krushkal and P. Teichner that the analogous
criterion for r = 2 is false. We prove a lemma on singular higher-dimensional
Borromean rings, yielding an elementary proof of the counterexample."
acknowledgement: Research supported by the Swiss National Science Foundation (Project
SNSF-PP00P2-138948), by the Austrian Science Fund (FWF Project P31312-N35), by the
Russian Foundation for Basic Research (Grants No. 15-01-06302 and 19-01-00169),
by a Simons-IUM Fellowship, and by the D. Zimin Dynasty Foundation Grant. We would
like to thank E. Alkin, A. Klyachko, V. Krushkal, S. Melikhov, M. Tancer, P. Teichner
and anonymous referees for helpful comments and discussions.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Sergey
full_name: Avvakumov, Sergey
id: 3827DAC8-F248-11E8-B48F-1D18A9856A87
last_name: Avvakumov
orcid: 0000-0002-7840-5062
- first_name: Isaac
full_name: Mabillard, Isaac
id: 32BF9DAA-F248-11E8-B48F-1D18A9856A87
last_name: Mabillard
- first_name: Arkadiy B.
full_name: Skopenkov, Arkadiy B.
last_name: Skopenkov
- first_name: Uli
full_name: Wagner, Uli
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
citation:
ama: Avvakumov S, Mabillard I, Skopenkov AB, Wagner U. Eliminating higher-multiplicity
intersections. III. Codimension 2. Israel Journal of Mathematics. 2021;245:501–534.
doi:10.1007/s11856-021-2216-z
apa: Avvakumov, S., Mabillard, I., Skopenkov, A. B., & Wagner, U. (2021). Eliminating
higher-multiplicity intersections. III. Codimension 2. Israel Journal of Mathematics.
Springer Nature. https://doi.org/10.1007/s11856-021-2216-z
chicago: Avvakumov, Sergey, Isaac Mabillard, Arkadiy B. Skopenkov, and Uli Wagner.
“Eliminating Higher-Multiplicity Intersections. III. Codimension 2.” Israel
Journal of Mathematics. Springer Nature, 2021. https://doi.org/10.1007/s11856-021-2216-z.
ieee: S. Avvakumov, I. Mabillard, A. B. Skopenkov, and U. Wagner, “Eliminating higher-multiplicity
intersections. III. Codimension 2,” Israel Journal of Mathematics, vol.
245. Springer Nature, pp. 501–534, 2021.
ista: Avvakumov S, Mabillard I, Skopenkov AB, Wagner U. 2021. Eliminating higher-multiplicity
intersections. III. Codimension 2. Israel Journal of Mathematics. 245, 501–534.
mla: Avvakumov, Sergey, et al. “Eliminating Higher-Multiplicity Intersections. III.
Codimension 2.” Israel Journal of Mathematics, vol. 245, Springer Nature,
2021, pp. 501–534, doi:10.1007/s11856-021-2216-z.
short: S. Avvakumov, I. Mabillard, A.B. Skopenkov, U. Wagner, Israel Journal of
Mathematics 245 (2021) 501–534.
corr_author: '1'
date_created: 2021-11-07T23:01:24Z
date_published: 2021-10-30T00:00:00Z
date_updated: 2025-07-02T10:54:52Z
day: '30'
department:
- _id: UlWa
doi: 10.1007/s11856-021-2216-z
external_id:
arxiv:
- '1511.03501'
isi:
- '000712942100013'
intvolume: ' 245'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1511.03501
month: '10'
oa: 1
oa_version: Preprint
page: '501–534 '
project:
- _id: 26611F5C-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P31312
name: Algorithms for Embeddings and Homotopy Theory
publication: Israel Journal of Mathematics
publication_identifier:
eissn:
- 1565-8511
issn:
- 0021-2172
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '9308'
relation: earlier_version
status: public
- id: '8183'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Eliminating higher-multiplicity intersections. III. Codimension 2
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 245
year: '2021'
...
---
_id: '7806'
abstract:
- lang: eng
text: "We consider the following decision problem EMBEDk→d in computational topology
(where k ≤ d are fixed positive integers): Given a finite simplicial complex K
of dimension k, does there exist a (piecewise-linear) embedding of K into ℝd?\r\nThe
special case EMBED1→2 is graph planarity, which is decidable in linear time, as
shown by Hopcroft and Tarjan. In higher dimensions, EMBED2→3 and EMBED3→3 are
known to be decidable (as well as NP-hard), and recent results of Čadek et al.
in computational homotopy theory, in combination with the classical Haefliger–Weber
theorem in geometric topology, imply that EMBEDk→d can be solved in polynomial
time for any fixed pair (k, d) of dimensions in the so-called metastable range
.\r\nHere, by contrast, we prove that EMBEDk→d is algorithmically undecidable
for almost all pairs of dimensions outside the metastable range, namely for .
This almost completely resolves the decidability vs. undecidability of EMBEDk→d
in higher dimensions and establishes a sharp dichotomy between polynomial-time
solvability and undecidability.\r\nOur result complements (and in a wide range
of dimensions strengthens) earlier results of Matoušek, Tancer, and the second
author, who showed that EMBEDk→d is undecidable for 4 ≤ k ϵ {d – 1, d}, and NP-hard
for all remaining pairs (k, d) outside the metastable range and satisfying d ≥
4."
article_processing_charge: No
author:
- first_name: Marek
full_name: Filakovský, Marek
id: 3E8AF77E-F248-11E8-B48F-1D18A9856A87
last_name: Filakovský
- first_name: Uli
full_name: Wagner, Uli
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
- first_name: Stephan Y
full_name: Zhechev, Stephan Y
id: 3AA52972-F248-11E8-B48F-1D18A9856A87
last_name: Zhechev
citation:
ama: 'Filakovský M, Wagner U, Zhechev SY. Embeddability of simplicial complexes
is undecidable. In: Proceedings of the Annual ACM-SIAM Symposium on Discrete
Algorithms. Vol 2020-January. SIAM; 2020:767-785. doi:10.1137/1.9781611975994.47'
apa: 'Filakovský, M., Wagner, U., & Zhechev, S. Y. (2020). Embeddability of
simplicial complexes is undecidable. In Proceedings of the Annual ACM-SIAM
Symposium on Discrete Algorithms (Vol. 2020–January, pp. 767–785). Salt Lake
City, UT, United States: SIAM. https://doi.org/10.1137/1.9781611975994.47'
chicago: Filakovský, Marek, Uli Wagner, and Stephan Y Zhechev. “Embeddability of
Simplicial Complexes Is Undecidable.” In Proceedings of the Annual ACM-SIAM
Symposium on Discrete Algorithms, 2020–January:767–85. SIAM, 2020. https://doi.org/10.1137/1.9781611975994.47.
ieee: M. Filakovský, U. Wagner, and S. Y. Zhechev, “Embeddability of simplicial
complexes is undecidable,” in Proceedings of the Annual ACM-SIAM Symposium
on Discrete Algorithms, Salt Lake City, UT, United States, 2020, vol. 2020–January,
pp. 767–785.
ista: 'Filakovský M, Wagner U, Zhechev SY. 2020. Embeddability of simplicial complexes
is undecidable. Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms.
SODA: Symposium on Discrete Algorithms vol. 2020–January, 767–785.'
mla: Filakovský, Marek, et al. “Embeddability of Simplicial Complexes Is Undecidable.”
Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, vol.
2020–January, SIAM, 2020, pp. 767–85, doi:10.1137/1.9781611975994.47.
short: M. Filakovský, U. Wagner, S.Y. Zhechev, in:, Proceedings of the Annual ACM-SIAM
Symposium on Discrete Algorithms, SIAM, 2020, pp. 767–785.
conference:
end_date: 2020-01-08
location: Salt Lake City, UT, United States
name: 'SODA: Symposium on Discrete Algorithms'
start_date: 2020-01-05
date_created: 2020-05-10T22:00:48Z
date_published: 2020-01-01T00:00:00Z
date_updated: 2026-06-18T19:27:16Z
day: '01'
ddc:
- '500'
department:
- _id: UlWa
doi: 10.1137/1.9781611975994.47
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1137/1.9781611975994.47
month: '01'
oa: 1
oa_version: Published Version
page: 767-785
project:
- _id: 26611F5C-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P31312
name: Algorithms for Embeddings and Homotopy Theory
publication: Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
publication_identifier:
isbn:
- '9781611975994'
publication_status: published
publisher: SIAM
quality_controlled: '1'
scopus_import: '1'
status: public
title: Embeddability of simplicial complexes is undecidable
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2020-January
year: '2020'
...
---
_id: '7991'
abstract:
- lang: eng
text: 'We define and study a discrete process that generalizes the convex-layer
decomposition of a planar point set. Our process, which we call homotopic curve
shortening (HCS), starts with a closed curve (which might self-intersect) in the
presence of a set P⊂ ℝ² of point obstacles, and evolves in discrete steps, where
each step consists of (1) taking shortcuts around the obstacles, and (2) reducing
the curve to its shortest homotopic equivalent. We find experimentally that, if
the initial curve is held fixed and P is chosen to be either a very fine regular
grid or a uniformly random point set, then HCS behaves at the limit like the affine
curve-shortening flow (ACSF). This connection between HCS and ACSF generalizes
the link between "grid peeling" and the ACSF observed by Eppstein et al. (2017),
which applied only to convex curves, and which was studied only for regular grids.
We prove that HCS satisfies some properties analogous to those of ACSF: HCS is
invariant under affine transformations, preserves convexity, and does not increase
the total absolute curvature. Furthermore, the number of self-intersections of
a curve, or intersections between two curves (appropriately defined), does not
increase. Finally, if the initial curve is simple, then the number of inflection
points (appropriately defined) does not increase.'
alternative_title:
- LIPIcs
article_number: 12:1 - 12:15
article_processing_charge: No
arxiv: 1
author:
- first_name: Sergey
full_name: Avvakumov, Sergey
id: 3827DAC8-F248-11E8-B48F-1D18A9856A87
last_name: Avvakumov
orcid: 0000-0002-7840-5062
- first_name: Gabriel
full_name: Nivasch, Gabriel
last_name: Nivasch
citation:
ama: 'Avvakumov S, Nivasch G. Homotopic curve shortening and the affine curve-shortening
flow. In: 36th International Symposium on Computational Geometry. Vol 164.
Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2020. doi:10.4230/LIPIcs.SoCG.2020.12'
apa: 'Avvakumov, S., & Nivasch, G. (2020). Homotopic curve shortening and the
affine curve-shortening flow. In 36th International Symposium on Computational
Geometry (Vol. 164). Zürich, Switzerland: Schloss Dagstuhl - Leibniz-Zentrum
für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2020.12'
chicago: Avvakumov, Sergey, and Gabriel Nivasch. “Homotopic Curve Shortening and
the Affine Curve-Shortening Flow.” In 36th International Symposium on Computational
Geometry, Vol. 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020.
https://doi.org/10.4230/LIPIcs.SoCG.2020.12.
ieee: S. Avvakumov and G. Nivasch, “Homotopic curve shortening and the affine curve-shortening
flow,” in 36th International Symposium on Computational Geometry, Zürich,
Switzerland, 2020, vol. 164.
ista: 'Avvakumov S, Nivasch G. 2020. Homotopic curve shortening and the affine curve-shortening
flow. 36th International Symposium on Computational Geometry. SoCG: Symposium
on Computational Geometry, LIPIcs, vol. 164, 12:1-12:15.'
mla: Avvakumov, Sergey, and Gabriel Nivasch. “Homotopic Curve Shortening and the
Affine Curve-Shortening Flow.” 36th International Symposium on Computational
Geometry, vol. 164, 12:1-12:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2020, doi:10.4230/LIPIcs.SoCG.2020.12.
short: S. Avvakumov, G. Nivasch, in:, 36th International Symposium on Computational
Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020.
conference:
end_date: 2020-06-26
location: Zürich, Switzerland
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2020-06-22
date_created: 2020-06-22T09:14:19Z
date_published: 2020-06-01T00:00:00Z
date_updated: 2025-07-10T11:54:56Z
day: '01'
ddc:
- '510'
department:
- _id: UlWa
doi: 10.4230/LIPIcs.SoCG.2020.12
external_id:
arxiv:
- '1909.00263'
file:
- access_level: open_access
checksum: 6872df6549142f709fb6354a1b2f2c06
content_type: application/pdf
creator: dernst
date_created: 2020-06-23T11:13:49Z
date_updated: 2020-07-14T12:48:06Z
file_id: '8007'
file_name: 2020_LIPIcsSoCG_Avvakumov.pdf
file_size: 575896
relation: main_file
file_date_updated: 2020-07-14T12:48:06Z
has_accepted_license: '1'
intvolume: ' 164'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/3.0/
month: '06'
oa: 1
oa_version: Published Version
project:
- _id: 26611F5C-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P31312
name: Algorithms for Embeddings and Homotopy Theory
publication: 36th International Symposium on Computational Geometry
publication_identifier:
isbn:
- '9783959771436'
issn:
- 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
scopus_import: '1'
status: public
title: Homotopic curve shortening and the affine curve-shortening flow
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/3.0/legalcode
name: Creative Commons Attribution 3.0 Unported (CC BY 3.0)
short: CC BY (3.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 164
year: '2020'
...
---
_id: '6563'
abstract:
- lang: eng
text: "This paper presents two algorithms. The first decides the existence of a
pointed homotopy between given simplicial maps \U0001D453,\U0001D454:\U0001D44B→\U0001D44C,
and the second computes the group [\U0001D6F4\U0001D44B,\U0001D44C]∗ of pointed
homotopy classes of maps from a suspension; in both cases, the target Y is assumed
simply connected. More generally, these algorithms work relative to \U0001D434⊆\U0001D44B."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Marek
full_name: Filakovský, Marek
id: 3E8AF77E-F248-11E8-B48F-1D18A9856A87
last_name: Filakovský
- first_name: Lukas
full_name: Vokřínek, Lukas
last_name: Vokřínek
citation:
ama: Filakovský M, Vokřínek L. Are two given maps homotopic? An algorithmic viewpoint.
Foundations of Computational Mathematics. 2020;20:311-330. doi:10.1007/s10208-019-09419-x
apa: Filakovský, M., & Vokřínek, L. (2020). Are two given maps homotopic? An
algorithmic viewpoint. Foundations of Computational Mathematics. Springer
Nature. https://doi.org/10.1007/s10208-019-09419-x
chicago: Filakovský, Marek, and Lukas Vokřínek. “Are Two given Maps Homotopic? An
Algorithmic Viewpoint.” Foundations of Computational Mathematics. Springer
Nature, 2020. https://doi.org/10.1007/s10208-019-09419-x.
ieee: M. Filakovský and L. Vokřínek, “Are two given maps homotopic? An algorithmic
viewpoint,” Foundations of Computational Mathematics, vol. 20. Springer
Nature, pp. 311–330, 2020.
ista: Filakovský M, Vokřínek L. 2020. Are two given maps homotopic? An algorithmic
viewpoint. Foundations of Computational Mathematics. 20, 311–330.
mla: Filakovský, Marek, and Lukas Vokřínek. “Are Two given Maps Homotopic? An Algorithmic
Viewpoint.” Foundations of Computational Mathematics, vol. 20, Springer
Nature, 2020, pp. 311–30, doi:10.1007/s10208-019-09419-x.
short: M. Filakovský, L. Vokřínek, Foundations of Computational Mathematics 20 (2020)
311–330.
date_created: 2019-06-16T21:59:14Z
date_published: 2020-04-01T00:00:00Z
date_updated: 2025-07-10T11:53:32Z
day: '01'
department:
- _id: UlWa
doi: 10.1007/s10208-019-09419-x
external_id:
arxiv:
- '1312.2337'
isi:
- '000522437400004'
intvolume: ' 20'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1312.2337
month: '04'
oa: 1
oa_version: Preprint
page: 311-330
project:
- _id: 26611F5C-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P31312
name: Algorithms for Embeddings and Homotopy Theory
publication: Foundations of Computational Mathematics
publication_identifier:
eissn:
- 1615-3383
issn:
- 1615-3375
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Are two given maps homotopic? An algorithmic viewpoint
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 20
year: '2020'
...
---
_id: '8182'
abstract:
- lang: eng
text: "Suppose that $n\\neq p^k$ and $n\\neq 2p^k$ for all $k$ and all primes $p$.
We prove that for any Hausdorff compactum $X$ with a free action of the symmetric
group $\\mathfrak S_n$ there exists an $\\mathfrak S_n$-equivariant map $X \\to\r\n{\\mathbb
R}^n$ whose image avoids the diagonal $\\{(x,x\\dots,x)\\in {\\mathbb R}^n|x\\in
{\\mathbb R}\\}$.\r\n Previously, the special cases of this statement for certain
$X$ were usually proved using the equivartiant obstruction theory. Such calculations
are difficult and may become infeasible past the first (primary) obstruction.
We\r\ntake a different approach which allows us to prove the vanishing of all
obstructions simultaneously. The essential step in the proof is classifying the
possible degrees of $\\mathfrak S_n$-equivariant maps from the boundary\r\n$\\partial\\Delta^{n-1}$
of $(n-1)$-simplex to itself. Existence of equivariant maps between spaces is
important for many questions arising from discrete mathematics and geometry, such
as Kneser's conjecture, the Square Peg conjecture, the Splitting Necklace problem,
and the Topological Tverberg conjecture, etc. We demonstrate the utility of our
result applying it to one such question, a specific instance of envy-free division
problem."
article_number: '1910.12628'
article_processing_charge: No
arxiv: 1
author:
- first_name: Sergey
full_name: Avvakumov, Sergey
id: 3827DAC8-F248-11E8-B48F-1D18A9856A87
last_name: Avvakumov
orcid: 0000-0002-7840-5062
- first_name: Sergey
full_name: Kudrya, Sergey
id: ecf01965-d252-11ea-95a5-8ada5f6c6a67
last_name: Kudrya
citation:
ama: Avvakumov S, Kudrya S. Vanishing of all equivariant obstructions and the mapping
degree. arXiv. doi:10.48550/arXiv.1910.12628
apa: Avvakumov, S., & Kudrya, S. (n.d.). Vanishing of all equivariant obstructions
and the mapping degree. arXiv. https://doi.org/10.48550/arXiv.1910.12628
chicago: Avvakumov, Sergey, and Sergey Kudrya. “Vanishing of All Equivariant Obstructions
and the Mapping Degree.” ArXiv, n.d. https://doi.org/10.48550/arXiv.1910.12628.
ieee: S. Avvakumov and S. Kudrya, “Vanishing of all equivariant obstructions and
the mapping degree,” arXiv. .
ista: Avvakumov S, Kudrya S. Vanishing of all equivariant obstructions and the mapping
degree. arXiv, 1910.12628.
mla: Avvakumov, Sergey, and Sergey Kudrya. “Vanishing of All Equivariant Obstructions
and the Mapping Degree.” ArXiv, 1910.12628, doi:10.48550/arXiv.1910.12628.
short: S. Avvakumov, S. Kudrya, ArXiv (n.d.).
corr_author: '1'
date_created: 2020-07-30T10:45:08Z
date_published: 2019-10-28T00:00:00Z
date_updated: 2026-04-08T07:25:54Z
day: '28'
department:
- _id: UlWa
doi: 10.48550/arXiv.1910.12628
external_id:
arxiv:
- '1910.12628'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1910.12628
month: '10'
oa: 1
oa_version: Preprint
project:
- _id: 26611F5C-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P31312
name: Algorithms for Embeddings and Homotopy Theory
publication: arXiv
publication_status: draft
related_material:
record:
- id: '11446'
relation: later_version
status: public
- id: '8156'
relation: dissertation_contains
status: public
status: public
title: Vanishing of all equivariant obstructions and the mapping degree
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2019'
...
---
_id: '8184'
abstract:
- lang: eng
text: "Denote by ∆N the N-dimensional simplex. A map f : ∆N → Rd is an almost r-embedding
if fσ1∩. . .∩fσr = ∅ whenever σ1, . . . , σr are pairwise disjoint faces. A counterexample
to the topological Tverberg conjecture asserts that if r is not a prime power
and d ≥ 2r + 1, then there is an almost r-embedding ∆(d+1)(r−1) → Rd. This was
improved by Blagojevi´c–Frick–Ziegler using a simple construction of higher-dimensional
counterexamples by taking k-fold join power of lower-dimensional ones. We improve
this further (for d large compared to r): If r is not a prime power and N := (d+
1)r−r l\r\nd + 2 r + 1 m−2, then there is an almost r-embedding ∆N → Rd. For the
r-fold van Kampen–Flores conjecture we also produce counterexamples which are
stronger than previously known. Our proof is based on generalizations of the Mabillard–Wagner
theorem on construction of almost r-embeddings from equivariant maps, and of the
Ozaydin theorem on existence of equivariant maps. "
acknowledgement: We would like to thank F. Frick for helpful discussions
article_number: '1908.08731'
article_processing_charge: No
arxiv: 1
author:
- first_name: Sergey
full_name: Avvakumov, Sergey
id: 3827DAC8-F248-11E8-B48F-1D18A9856A87
last_name: Avvakumov
orcid: 0000-0002-7840-5062
- first_name: R.
full_name: Karasev, R.
last_name: Karasev
- first_name: A.
full_name: Skopenkov, A.
last_name: Skopenkov
citation:
ama: Avvakumov S, Karasev R, Skopenkov A. Stronger counterexamples to the topological
Tverberg conjecture. arXiv. doi:10.48550/arXiv.1908.08731
apa: Avvakumov, S., Karasev, R., & Skopenkov, A. (n.d.). Stronger counterexamples
to the topological Tverberg conjecture. arXiv. https://doi.org/10.48550/arXiv.1908.08731
chicago: Avvakumov, Sergey, R. Karasev, and A. Skopenkov. “Stronger Counterexamples
to the Topological Tverberg Conjecture.” ArXiv, n.d. https://doi.org/10.48550/arXiv.1908.08731.
ieee: S. Avvakumov, R. Karasev, and A. Skopenkov, “Stronger counterexamples to the
topological Tverberg conjecture,” arXiv. .
ista: Avvakumov S, Karasev R, Skopenkov A. Stronger counterexamples to the topological
Tverberg conjecture. arXiv, 1908.08731.
mla: Avvakumov, Sergey, et al. “Stronger Counterexamples to the Topological Tverberg
Conjecture.” ArXiv, 1908.08731, doi:10.48550/arXiv.1908.08731.
short: S. Avvakumov, R. Karasev, A. Skopenkov, ArXiv (n.d.).
date_created: 2020-07-30T10:45:34Z
date_published: 2019-08-23T00:00:00Z
date_updated: 2026-04-08T07:25:54Z
day: '23'
department:
- _id: UlWa
doi: 10.48550/arXiv.1908.08731
external_id:
arxiv:
- '1908.08731'
isi:
- '000986519600004'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1908.08731
month: '08'
oa: 1
oa_version: Preprint
project:
- _id: 26611F5C-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P31312
name: Algorithms for Embeddings and Homotopy Theory
publication: arXiv
publication_status: draft
related_material:
record:
- id: '8156'
relation: dissertation_contains
status: public
status: public
title: Stronger counterexamples to the topological Tverberg conjecture
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2019'
...
---
_id: '8185'
abstract:
- lang: eng
text: "In this paper we study envy-free division problems. The classical approach
to some of such problems, used by David Gale, reduces to considering continuous
maps of a simplex to itself and finding sufficient conditions when this map hits
the center of the simplex. The mere continuity is not sufficient for such a conclusion,
the usual assumption (for example, in the Knaster--Kuratowski--Mazurkiewicz and
the Gale theorem) is a certain boundary condition.\r\n We follow Erel Segal-Halevi,
Fr\\'ed\\'eric Meunier, and Shira Zerbib, and replace the boundary condition by
another assumption, which has the economic meaning of possibility for a player
to prefer an empty part in the segment\r\npartition problem. We solve the problem
positively when $n$, the number of players that divide the segment, is a prime
power, and we provide counterexamples for every $n$ which is not a prime power.
We also provide counterexamples relevant to a wider class of fair or envy-free
partition problems when $n$ is odd and not a prime power."
article_number: '1907.11183'
article_processing_charge: No
arxiv: 1
author:
- first_name: Sergey
full_name: Avvakumov, Sergey
id: 3827DAC8-F248-11E8-B48F-1D18A9856A87
last_name: Avvakumov
orcid: 0000-0002-7840-5062
- first_name: Roman
full_name: Karasev, Roman
last_name: Karasev
citation:
ama: Avvakumov S, Karasev R. Envy-free division using mapping degree. arXiv.
doi:10.48550/arXiv.1907.11183
apa: Avvakumov, S., & Karasev, R. (n.d.). Envy-free division using mapping degree.
arXiv. https://doi.org/10.48550/arXiv.1907.11183
chicago: Avvakumov, Sergey, and Roman Karasev. “Envy-Free Division Using Mapping
Degree.” ArXiv, n.d. https://doi.org/10.48550/arXiv.1907.11183.
ieee: S. Avvakumov and R. Karasev, “Envy-free division using mapping degree,” arXiv.
.
ista: Avvakumov S, Karasev R. Envy-free division using mapping degree. arXiv, 1907.11183.
mla: Avvakumov, Sergey, and Roman Karasev. “Envy-Free Division Using Mapping Degree.”
ArXiv, 1907.11183, doi:10.48550/arXiv.1907.11183.
short: S. Avvakumov, R. Karasev, ArXiv (n.d.).
corr_author: '1'
date_created: 2020-07-30T10:45:51Z
date_published: 2019-07-25T00:00:00Z
date_updated: 2026-04-08T07:25:54Z
day: '25'
department:
- _id: UlWa
doi: 10.48550/arXiv.1907.11183
external_id:
arxiv:
- '1907.11183'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1907.11183
month: '07'
oa: 1
oa_version: Preprint
project:
- _id: 26611F5C-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P31312
name: Algorithms for Embeddings and Homotopy Theory
publication: arXiv
publication_status: draft
related_material:
link:
- relation: later_version
url: https://doi.org/10.1112/mtk.12059
record:
- id: '8156'
relation: dissertation_contains
status: public
status: public
title: Envy-free division using mapping degree
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2019'
...