---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '22406'
abstract:
- lang: eng
text: "It is known that for a uniform morphic sequence \U0001D496 =⟨\U0001D462\U0001D45B⟩∞\r\n\U0001D45B=0
and an algebraic number \U0001D6FD such that |\U0001D6FD| >1, the number [[\U0001D496]]\U0001D6FD
:=∑∞\r\n\U0001D45B=0(\U0001D462\U0001D45B/\U0001D6FD\U0001D45B) either lies in
ℚ(\U0001D6FD) or is transcendental. In this paper, we show a similar rational–transcendental
dichotomy for sequences defined by irreducible Pisot morphisms on binary alphabets.
Subject to the Pisot conjecture (an irreducible Pisot morphism has pure discrete
spectrum), we generalise the latter result to arbitrary finite alphabets. In certain
cases, we are able to show transcendence of [[\U0001D496]]\U0001D6FD outright.
In particular, for \U0001D458 ≥2, if \U0001D496 is the k-Bonacci word, then [[\U0001D496]]\U0001D6FD
is transcendental."
acknowledgement: "We thank the anonymous referee for identifying an error in an earlier\r\nversion
of the paper. We gratefully acknowledge support from UKRI Frontier Research\r\nGrant
EP/X033813/1, ERC grant DynAMiCS (101167561) and DFG grant 389792660 as\r\npart
of TRR 248. J.O. is also affiliated with Keble College, Oxford as an Emmy Network\r\nfellow."
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Pavol
full_name: Kebis, Pavol
id: 2e0132b3-4e98-11ef-b275-cf7281c2802a
last_name: Kebis
- first_name: FLORIAN
full_name: LUCA, FLORIAN
last_name: LUCA
- first_name: JOEL
full_name: OUAKNINE, JOEL
last_name: OUAKNINE
- first_name: ANDREW
full_name: SCOONES, ANDREW
last_name: SCOONES
- first_name: JAMES
full_name: WORRELL, JAMES
last_name: WORRELL
citation:
ama: Kebis P, LUCA F, OUAKNINE J, SCOONES A, WORRELL J. Transcendence for Pisot
morphic words over an algebraic base. Ergodic Theory and Dynamical Systems.
2026:1-22. doi:10.1017/etds.2026.10324
apa: Kebis, P., LUCA, F., OUAKNINE, J., SCOONES, A., & WORRELL, J. (2026). Transcendence
for Pisot morphic words over an algebraic base. Ergodic Theory and Dynamical
Systems. Cambridge University Press. https://doi.org/10.1017/etds.2026.10324
chicago: Kebis, Pavol, FLORIAN LUCA, JOEL OUAKNINE, ANDREW SCOONES, and JAMES WORRELL.
“Transcendence for Pisot Morphic Words over an Algebraic Base.” Ergodic Theory
and Dynamical Systems. Cambridge University Press, 2026. https://doi.org/10.1017/etds.2026.10324.
ieee: P. Kebis, F. LUCA, J. OUAKNINE, A. SCOONES, and J. WORRELL, “Transcendence
for Pisot morphic words over an algebraic base,” Ergodic Theory and Dynamical
Systems. Cambridge University Press, pp. 1–22, 2026.
ista: Kebis P, LUCA F, OUAKNINE J, SCOONES A, WORRELL J. 2026. Transcendence for
Pisot morphic words over an algebraic base. Ergodic Theory and Dynamical Systems.,
1–22.
mla: Kebis, Pavol, et al. “Transcendence for Pisot Morphic Words over an Algebraic
Base.” Ergodic Theory and Dynamical Systems, Cambridge University Press,
2026, pp. 1–22, doi:10.1017/etds.2026.10324.
short: P. Kebis, F. LUCA, J. OUAKNINE, A. SCOONES, J. WORRELL, Ergodic Theory and
Dynamical Systems (2026) 1–22.
das_tickbox: '0'
date_created: 2026-07-27T05:53:25Z
date_published: 2026-07-10T00:00:00Z
date_updated: 2026-08-03T06:17:50Z
day: '10'
ddc:
- '000'
department:
- _id: ToHe
- _id: GradSch
doi: 10.1017/etds.2026.10324
external_id:
arxiv:
- '2405.05279'
fulldoi: https://doi.org/10.1017/etds.2026.10324
has_accepted_license: '1'
keyword:
- balanced-pair algorithm
- Cobham’s conjecture
- k-Bonacci words
- Pisot conjecture
- subspace theorem
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1017/etds.2026.10324
mathsc:
- 11J81
- 37B10
- 11J87
month: '07'
oa: 1
oa_version: Published Version
page: 1-22
publication: Ergodic Theory and Dynamical Systems
publication_identifier:
eissn:
- 1469-4417
issn:
- 0143-3857
publication_status: epub_ahead
publisher: Cambridge University Press
quality_controlled: '1'
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: no
title: Transcendence for Pisot morphic words over an algebraic base
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
year: '2026'
...
---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '22693'
abstract:
- lang: eng
text: We study torus-equivariant algebraic K-theory of affine Schubert varieties
in the perfect affine Grassmannians over Fp. We further compare it to the torus-equivariant
Hochschild homology of perfect complexes, which has a geometric description in
terms of global functions on certain fixed-point schemes. We prove that Fp-linearly,
this comparison is an isomorphism. Our approach is quite constructive, resulting
in new computations of these K-theory rings. We establish various structural results
for equivariant perfect algebraic K-theory on the way; we believe these are of
independent interest.
acknowledgement: "I would like to thank the following people for fruitful discussions,\r\nhelpful
sanity checks or comments on previous drafts: Roman Bezrukavnikov, Jens Niklas Eberhardt,
Mischa Elkner, Tamás Hausel, Andres Fernandez Herrero, Adeel Khan,\r\nBernhard Köck,
Andrei Konovalov, Quoc Ho, Mirko Mauri, Matthew Morrow, Charanya\r\nRavi, Kamil
Rychlewicz, Shyiu Shen, Vladimir Sosnilo, Georg Tamme, Xinwen Zhu. I\r\nwould further
like to thank Marc Hoyois and the anonymous referee for spotting an error\r\nin
a previous version.\r\nThis work was done during author’s PhD at the Institute of
Science and Technology Austria (ISTA). It was funded by a DOC Fellowship of the
Austrian Academy\r\nof Sciences and by the Austrian Science Fund (FWF) 10.55776/P35847.
For open access\r\npurposes, the author has applied a CC BY public copyright license
to any author-accepted\r\nmanuscript version arising from this submission."
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Jakub
full_name: Löwit, Jakub
id: e3b80ae2-eb8e-11eb-b029-9aef4a9108a0
last_name: Löwit
citation:
ama: Löwit J. Equivariant K-theory, affine Grassmannian and perfection. Documenta
Mathematica. 2026. doi:10.4171/dm/1064
apa: Löwit, J. (2026). Equivariant K-theory, affine Grassmannian and perfection.
Documenta Mathematica. EMS Press. https://doi.org/10.4171/dm/1064
chicago: Löwit, Jakub. “Equivariant K-Theory, Affine Grassmannian and Perfection.”
Documenta Mathematica. EMS Press, 2026. https://doi.org/10.4171/dm/1064.
ieee: J. Löwit, “Equivariant K-theory, affine Grassmannian and perfection,” Documenta
Mathematica. EMS Press, 2026.
ista: Löwit J. 2026. Equivariant K-theory, affine Grassmannian and perfection. Documenta
Mathematica.
mla: Löwit, Jakub. “Equivariant K-Theory, Affine Grassmannian and Perfection.” Documenta
Mathematica, EMS Press, 2026, doi:10.4171/dm/1064.
short: J. Löwit, Documenta Mathematica (2026).
corr_author: '1'
das_tickbox: '0'
date_created: 2026-08-12T13:29:17Z
date_published: 2026-03-26T00:00:00Z
date_updated: 2026-08-26T06:53:54Z
day: '26'
ddc:
- '500'
department:
- _id: GradSch
- _id: TaHa
doi: 10.4171/dm/1064
external_id:
arxiv:
- '2409.18925'
fulldoi: https://doi.org/10.4171/dm/1064
has_accepted_license: '1'
keyword:
- equivariant algebraic K-theory
- perfection in positive characteristic
- affine Grassmannian
- affine Schubert varieties
- Dennis trace map
- equivariant Hochschild homology
- fixed-point schemes
- toric varieties
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.4171/DM/1064
mathsc:
- '19E08'
- 19L47
- 20G44
- 14G17
- 19D55
- 14F43
- 14L30
- 14D24
- 14M25
month: '03'
oa: 1
oa_version: Published Version
project:
- _id: 34b2c9cb-11ca-11ed-8bc3-a50ba74ca4a3
grant_number: P35847
name: Geometry of the tip of the global nilpotent cone
publication: Documenta Mathematica
publication_identifier:
eissn:
- 1431-0643
issn:
- 1431-0635
publication_status: epub_ahead
publisher: EMS Press
quality_controlled: '1'
related_material:
record:
- id: '22694'
relation: dissertation_contains
status: public
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: no
title: Equivariant K-theory, affine Grassmannian and perfection
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
year: '2026'
...
---
_id: '22373'
abstract:
- lang: eng
text: "Data dissemination is a fundamental task in distributed computing. This paper
studies broadcast problems in various innovative models where the communication
network connecting n processes is dynamic (e.g., due to mobility or failures)
and controlled by an adversary. \r\nIn the first model, the processes transitively
communicate their ids in synchronous rounds along a rooted tree given in each
round by the adversary whose goal is to maximize the number of rounds until at
least one id is known by all processes. Previous research has shown a ⌈(3n-1)/2⌉-2
lower bound and an O(nlog log n) upper bound. We show the first linear upper bound
for this problem, namely ⌈(1+√2) n-1⌉ ≈ 2.4n.\r\nWe extend these results to the
setting where the adversary gives in each round k-disjoint forests and their goal
is to maximize the number of rounds until there is a set of k ids such that each
process knows of at least one of them. We give a ⌈3(n-k)/2⌉-1 lower bound and
a (π²+6)/6 n+1 ≈ 2.6n upper bound for this problem.\r\nFinally, we study the setting
where the adversary gives in each round a directed graph with k roots and their
goal is to maximize the number of rounds until there exist k ids that are known
by all processes. We give a ⌈3(n-3k)/2⌉+2 lower bound and a ⌈(1+√2)n⌉+k-1 ≈ 2.4n+k
upper bound for this problem.\r\nFor the two latter problems no upper or lower
bounds were previously known."
acknowledgement: " This project has received funding from the European Research Council
(ERC) under\r\nthe European Union’s Horizon 2020 research and innovation programme
(grant agreement No.\r\n101019564). This work was further supported by the Austrian
Science Fund (FWF) and netIDEE\r\nSCIENCE project P 33775-N, as well as the FWF
project I 4800-N (ADVISE)"
alternative_title:
- LIPIcs
article_number: '47'
article_processing_charge: No
arxiv: 1
author:
- first_name: Antoine
full_name: El-Hayek, Antoine
id: 888a098e-fcac-11ee-aff7-d347be57b725
last_name: El-Hayek
orcid: 0000-0003-4268-7368
- first_name: Monika H
full_name: Henzinger, Monika H
id: 540c9bbd-f2de-11ec-812d-d04a5be85630
last_name: Henzinger
orcid: 0000-0002-5008-6530
- first_name: Stefan
full_name: Schmid, Stefan
last_name: Schmid
orcid: 0000-0002-7798-1711
citation:
ama: 'El-Hayek A, Henzinger M, Schmid S. Asymptotically tight bounds on the time
complexity of broadcast and its variants in dynamic networks. In: Tauman Kalai
Y, ed. 14th Innovations in Theoretical Computer Science Conference. Vol
251. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2023. doi:10.4230/LIPICS.ITCS.2023.47'
apa: 'El-Hayek, A., Henzinger, M., & Schmid, S. (2023). Asymptotically tight
bounds on the time complexity of broadcast and its variants in dynamic networks.
In Y. Tauman Kalai (Ed.), 14th Innovations in Theoretical Computer Science
Conference (Vol. 251). Cambridge, Massachusetts, USA: Schloss Dagstuhl - Leibniz-Zentrum
für Informatik. https://doi.org/10.4230/LIPICS.ITCS.2023.47'
chicago: El-Hayek, Antoine, Monika Henzinger, and Stefan Schmid. “Asymptotically
Tight Bounds on the Time Complexity of Broadcast and Its Variants in Dynamic Networks.”
In 14th Innovations in Theoretical Computer Science Conference, edited
by Yael Tauman Kalai, Vol. 251. Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2023. https://doi.org/10.4230/LIPICS.ITCS.2023.47.
ieee: A. El-Hayek, M. Henzinger, and S. Schmid, “Asymptotically tight bounds on
the time complexity of broadcast and its variants in dynamic networks,” in 14th
Innovations in Theoretical Computer Science Conference, Cambridge, Massachusetts,
USA, 2023, vol. 251.
ista: 'El-Hayek A, Henzinger M, Schmid S. 2023. Asymptotically tight bounds on the
time complexity of broadcast and its variants in dynamic networks. 14th Innovations
in Theoretical Computer Science Conference. ITCS: Innovations in Theoretical Computer
Science, LIPIcs, vol. 251, 47.'
mla: El-Hayek, Antoine, et al. “Asymptotically Tight Bounds on the Time Complexity
of Broadcast and Its Variants in Dynamic Networks.” 14th Innovations in Theoretical
Computer Science Conference, edited by Yael Tauman Kalai, vol. 251, 47, Schloss
Dagstuhl - Leibniz-Zentrum für Informatik, 2023, doi:10.4230/LIPICS.ITCS.2023.47.
short: A. El-Hayek, M. Henzinger, S. Schmid, in:, Y. Tauman Kalai (Ed.), 14th Innovations
in Theoretical Computer Science Conference, Schloss Dagstuhl - Leibniz-Zentrum
für Informatik, 2023.
conference:
end_date: 2023-01-13
location: Cambridge, Massachusetts, USA
name: 'ITCS: Innovations in Theoretical Computer Science'
start_date: 2023-01-10
date_created: 2026-07-20T11:45:04Z
date_published: 2023-02-01T00:00:00Z
date_updated: 2026-07-24T12:48:29Z
day: '01'
ddc:
- '000'
doi: 10.4230/LIPICS.ITCS.2023.47
editor:
- first_name: Yael
full_name: Tauman Kalai, Yael
last_name: Tauman Kalai
extern: '1'
external_id:
arxiv:
- '2211.10151'
file:
- access_level: open_access
checksum: d7f45fdcbc5fccd61db69f56d775c636
content_type: application/pdf
creator: cchlebak
date_created: 2026-07-22T08:04:03Z
date_updated: 2026-07-22T08:04:03Z
file_id: '22383'
file_name: 2023_LIPIcs_El-Hayek.pdf
file_size: 1077427
relation: main_file
success: 1
file_date_updated: 2026-07-22T08:04:03Z
fulldoi: https://doi.org/10.4230/LIPICS.ITCS.2023.47
has_accepted_license: '1'
intvolume: ' 251'
keyword:
- broadcast
- cover
- k-broadcast
- dynamic radius
- dynamic graphs
- oblivious message adversary
- time complexity
- Theory of computation → Distributed algorithms
- Networks → Network algorithms
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
publication: 14th Innovations in Theoretical Computer Science Conference
publication_identifier:
isbn:
- '9783959772631'
issn:
- 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
related_material:
record:
- id: '22281'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Asymptotically tight bounds on the time complexity of broadcast and its variants
in dynamic networks
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: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 251
year: '2023'
...
---
_id: '12151'
abstract:
- lang: eng
text: The k-sample G(k,W) from a graphon W:[0,1]2→[0,1] is the random graph on {1,…,k},
where we sample x1,…,xk∈[0,1] uniformly at random and make each pair {i,j}⊆{1,…,k}
an edge with probability W(xi,xj), with all these choices being mutually independent.
Let the random variable Xk(W) be the number of edges in G(k,W). Vera T. Sós asked
in 2012 whether two graphons U, W are necessarily weakly isomorphic if the random
variables Xk(U) and Xk(W) have the same distribution for every integer k≥2. This
question when one of the graphons W is a constant function was answered positively
by Endre Csóka and independently by Jacob Fox, Tomasz Łuczak and Vera T. Sós.
Here we investigate the question when W is a 2-step graphon and prove that the
answer is positive for a 3-dimensional family of such graphons. We also present
some related results.
acknowledgement: "Supported by Austrian Science Fund (FWF) Grant I3747. Supported
by ERC Advanced Grant 101020255 and Leverhulme Research Project Grant RPG-2018-424.\r\nAn
extended abstract of this paper appeared in the Proceedings of the European Conference\r\non
Combinatorics, Graph Theory and Applications (EuroComb 2021), CRM Research Perspectives,
Springer."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Oliver
full_name: Cooley, Oliver
id: 43f4ddd0-a46b-11ec-8df6-ef3703bd721d
last_name: Cooley
- first_name: M.
full_name: Kang, M.
last_name: Kang
- first_name: O.
full_name: Pikhurko, O.
last_name: Pikhurko
citation:
ama: Cooley O, Kang M, Pikhurko O. On a question of Vera T. Sós about size forcing
of graphons. Acta Mathematica Hungarica. 2022;168:1-26. doi:10.1007/s10474-022-01265-8
apa: Cooley, O., Kang, M., & Pikhurko, O. (2022). On a question of Vera T. Sós
about size forcing of graphons. Acta Mathematica Hungarica. Springer Nature.
https://doi.org/10.1007/s10474-022-01265-8
chicago: Cooley, Oliver, M. Kang, and O. Pikhurko. “On a Question of Vera T. Sós
about Size Forcing of Graphons.” Acta Mathematica Hungarica. Springer Nature,
2022. https://doi.org/10.1007/s10474-022-01265-8.
ieee: O. Cooley, M. Kang, and O. Pikhurko, “On a question of Vera T. Sós about size
forcing of graphons,” Acta Mathematica Hungarica, vol. 168. Springer Nature,
pp. 1–26, 2022.
ista: Cooley O, Kang M, Pikhurko O. 2022. On a question of Vera T. Sós about size
forcing of graphons. Acta Mathematica Hungarica. 168, 1–26.
mla: Cooley, Oliver, et al. “On a Question of Vera T. Sós about Size Forcing of
Graphons.” Acta Mathematica Hungarica, vol. 168, Springer Nature, 2022,
pp. 1–26, doi:10.1007/s10474-022-01265-8.
short: O. Cooley, M. Kang, O. Pikhurko, Acta Mathematica Hungarica 168 (2022) 1–26.
corr_author: '1'
date_created: 2023-01-12T12:07:59Z
date_published: 2022-11-23T00:00:00Z
date_updated: 2024-10-09T21:03:37Z
day: '23'
department:
- _id: MaKw
doi: 10.1007/s10474-022-01265-8
external_id:
arxiv:
- '2103.09114'
isi:
- '000886839900006'
fulldoi: https://doi.org/10.1007/s10474-022-01265-8
intvolume: ' 168'
isi: 1
keyword:
- graphon
- k-sample
- graphon forcing
- graph container
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.2103.09114'
month: '11'
oa: 1
oa_version: Preprint
page: 1-26
publication: Acta Mathematica Hungarica
publication_identifier:
eissn:
- 1588-2632
issn:
- 0236-5294
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: On a question of Vera T. Sós about size forcing of graphons
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 168
year: '2022'
...