---
_id: '15173'
abstract:
- lang: eng
  text: 'We show that the number of linear spaces on a set of n points and the number
    of rank-3 matroids on a ground set of size n are both of the form (cn+o(n))n2/6,
    where c=e3√/2−3(1+3–√)/2. This is the final piece of the puzzle for enumerating
    fixed-rank matroids at this level of accuracy: the numbers of rank-1 and rank-2
    matroids on a ground set of size n have exact representations in terms of well-known
    combinatorial functions, and it was recently proved by van der Hofstad, Pendavingh,
    and van der Pol that for constant r≥4 there are (e1−rn+o(n))nr−1/r! rank-r matroids
    on a ground set of size n. In our proof, we introduce a new approach for bounding
    the number of clique decompositions of a complete graph, using quasirandomness
    instead of the so-called entropy method that is common in this area.'
acknowledgement: "Sah and Sawhney were supported by NSF Graduate Research Fellowship
  Program DGE-1745302. Sah was supported by the PD Soros Fellowship.\r\nWe thank Michael
  Simkin for helpful comments on the manuscript. We thank Zach Hunter for\r\nseveral
  corrections."
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: Matthew Alan
  full_name: Kwan, Matthew Alan
  id: 5fca0887-a1db-11eb-95d1-ca9d5e0453b3
  last_name: Kwan
  orcid: 0000-0002-4003-7567
- first_name: Ashwin
  full_name: Sah, Ashwin
  last_name: Sah
- first_name: Mehtaab
  full_name: Sawhney, Mehtaab
  last_name: Sawhney
citation:
  ama: Kwan MA, Sah A, Sawhney M. Enumerating matroids and linear spaces. <i>Comptes
    Rendus Mathematique</i>. 2023;361(G2):565-575. doi:<a href="https://doi.org/10.5802/crmath.423">10.5802/crmath.423</a>
  apa: Kwan, M. A., Sah, A., &#38; Sawhney, M. (2023). Enumerating matroids and linear
    spaces. <i>Comptes Rendus Mathematique</i>. Academie des Sciences. <a href="https://doi.org/10.5802/crmath.423">https://doi.org/10.5802/crmath.423</a>
  chicago: Kwan, Matthew Alan, Ashwin Sah, and Mehtaab Sawhney. “Enumerating Matroids
    and Linear Spaces.” <i>Comptes Rendus Mathematique</i>. Academie des Sciences,
    2023. <a href="https://doi.org/10.5802/crmath.423">https://doi.org/10.5802/crmath.423</a>.
  ieee: M. A. Kwan, A. Sah, and M. Sawhney, “Enumerating matroids and linear spaces,”
    <i>Comptes Rendus Mathematique</i>, vol. 361, no. G2. Academie des Sciences, pp.
    565–575, 2023.
  ista: Kwan MA, Sah A, Sawhney M. 2023. Enumerating matroids and linear spaces. Comptes
    Rendus Mathematique. 361(G2), 565–575.
  mla: Kwan, Matthew Alan, et al. “Enumerating Matroids and Linear Spaces.” <i>Comptes
    Rendus Mathematique</i>, vol. 361, no. G2, Academie des Sciences, 2023, pp. 565–75,
    doi:<a href="https://doi.org/10.5802/crmath.423">10.5802/crmath.423</a>.
  short: M.A. Kwan, A. Sah, M. Sawhney, Comptes Rendus Mathematique 361 (2023) 565–575.
date_created: 2024-03-24T23:01:00Z
date_published: 2023-02-01T00:00:00Z
date_updated: 2025-09-09T14:26:32Z
day: '01'
ddc:
- '510'
department:
- _id: MaKw
doi: 10.5802/crmath.423
external_id:
  arxiv:
  - '2112.03788'
  isi:
  - '001167671400009'
file:
- access_level: open_access
  checksum: d1d0e0a854a79ae95fb66d75d9117a68
  content_type: application/pdf
  creator: dernst
  date_created: 2024-03-25T07:21:52Z
  date_updated: 2024-03-25T07:21:52Z
  file_id: '15174'
  file_name: 2023_ComptesRendusMath_Kwan.pdf
  file_size: 598097
  relation: main_file
  success: 1
file_date_updated: 2024-03-25T07:21:52Z
fulldoi: https://doi.org/10.5802/crmath.423
has_accepted_license: '1'
intvolume: '       361'
isi: 1
issue: G2
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
page: 565-575
publication: Comptes Rendus Mathematique
publication_identifier:
  eissn:
  - 1778-3569
  issn:
  - 1631-073X
publication_status: published
publisher: Academie des Sciences
quality_controlled: '1'
scopus_import: '1'
status: public
title: Enumerating matroids and linear spaces
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 361
year: '2023'
...
---
OA_place: repository
OA_type: green
_id: '22182'
abstract:
- lang: eng
  text: We present a short new proof of the canonical polynomial van der Waerden theorem,
    recently established by Girão.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Jacob
  full_name: Fox, Jacob
  last_name: Fox
- first_name: Yuval
  full_name: Wigderson, Yuval
  id: 2d0023a0-1567-11f0-833d-d5c1e476d4b5
  last_name: Wigderson
- first_name: Yufei
  full_name: Zhao, Yufei
  last_name: Zhao
citation:
  ama: Fox J, Wigderson Y, Zhao Y. A short proof of the canonical polynomial van der
    Waerden theorem. <i>Comptes Rendus Mathématique</i>. 2020;358(8):957-959. doi:<a
    href="https://doi.org/10.5802/crmath.101">10.5802/crmath.101</a>
  apa: Fox, J., Wigderson, Y., &#38; Zhao, Y. (2020). A short proof of the canonical
    polynomial van der Waerden theorem. <i>Comptes Rendus Mathématique</i>. Académie
    des Sciences. <a href="https://doi.org/10.5802/crmath.101">https://doi.org/10.5802/crmath.101</a>
  chicago: Fox, Jacob, Yuval Wigderson, and Yufei Zhao. “A Short Proof of the Canonical
    Polynomial van Der Waerden Theorem.” <i>Comptes Rendus Mathématique</i>. Académie
    des Sciences, 2020. <a href="https://doi.org/10.5802/crmath.101">https://doi.org/10.5802/crmath.101</a>.
  ieee: J. Fox, Y. Wigderson, and Y. Zhao, “A short proof of the canonical polynomial
    van der Waerden theorem,” <i>Comptes Rendus Mathématique</i>, vol. 358, no. 8.
    Académie des Sciences, pp. 957–959, 2020.
  ista: Fox J, Wigderson Y, Zhao Y. 2020. A short proof of the canonical polynomial
    van der Waerden theorem. Comptes Rendus Mathématique. 358(8), 957–959.
  mla: Fox, Jacob, et al. “A Short Proof of the Canonical Polynomial van Der Waerden
    Theorem.” <i>Comptes Rendus Mathématique</i>, vol. 358, no. 8, Académie des Sciences,
    2020, pp. 957–59, doi:<a href="https://doi.org/10.5802/crmath.101">10.5802/crmath.101</a>.
  short: J. Fox, Y. Wigderson, Y. Zhao, Comptes Rendus Mathématique 358 (2020) 957–959.
date_created: 2026-06-29T11:00:09Z
date_published: 2020-12-03T00:00:00Z
date_updated: 2026-07-14T09:19:20Z
day: '03'
doi: 10.5802/crmath.101
extern: '1'
external_id:
  arxiv:
  - '2005.04135'
fulldoi: https://doi.org/10.5802/crmath.101
intvolume: '       358'
issue: '8'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2005.04135
mathsc:
- 05D10
- 11B30
month: '12'
oa: 1
oa_version: Preprint
page: 957-959
publication: Comptes Rendus Mathématique
publication_identifier:
  eissn:
  - 1778-3569
  issn:
  - 1631-073X
publication_status: published
publisher: Académie des Sciences
quality_controlled: '1'
scopus_import: '1'
status: public
title: A short proof of the canonical polynomial van der Waerden theorem
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 358
year: '2020'
...
---
_id: '409'
abstract:
- lang: eng
  text: We give a simple proof of T. Stehling's result [4], whereby in any normal
    tiling of the plane with convex polygons with number of sides not less than six,
    all tiles except a finite number are hexagons.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Arseniy
  full_name: Akopyan, Arseniy
  id: 430D2C90-F248-11E8-B48F-1D18A9856A87
  last_name: Akopyan
  orcid: 0000-0002-2548-617X
citation:
  ama: Akopyan A. On the number of non-hexagons in a planar tiling. <i>Comptes Rendus
    Mathematique</i>. 2018;356(4):412-414. doi:<a href="https://doi.org/10.1016/j.crma.2018.03.005">10.1016/j.crma.2018.03.005</a>
  apa: Akopyan, A. (2018). On the number of non-hexagons in a planar tiling. <i>Comptes
    Rendus Mathematique</i>. Elsevier. <a href="https://doi.org/10.1016/j.crma.2018.03.005">https://doi.org/10.1016/j.crma.2018.03.005</a>
  chicago: Akopyan, Arseniy. “On the Number of Non-Hexagons in a Planar Tiling.” <i>Comptes
    Rendus Mathematique</i>. Elsevier, 2018. <a href="https://doi.org/10.1016/j.crma.2018.03.005">https://doi.org/10.1016/j.crma.2018.03.005</a>.
  ieee: A. Akopyan, “On the number of non-hexagons in a planar tiling,” <i>Comptes
    Rendus Mathematique</i>, vol. 356, no. 4. Elsevier, pp. 412–414, 2018.
  ista: Akopyan A. 2018. On the number of non-hexagons in a planar tiling. Comptes
    Rendus Mathematique. 356(4), 412–414.
  mla: Akopyan, Arseniy. “On the Number of Non-Hexagons in a Planar Tiling.” <i>Comptes
    Rendus Mathematique</i>, vol. 356, no. 4, Elsevier, 2018, pp. 412–14, doi:<a href="https://doi.org/10.1016/j.crma.2018.03.005">10.1016/j.crma.2018.03.005</a>.
  short: A. Akopyan, Comptes Rendus Mathematique 356 (2018) 412–414.
corr_author: '1'
date_created: 2018-12-11T11:46:19Z
date_published: 2018-04-01T00:00:00Z
date_updated: 2025-07-10T11:52:35Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.crma.2018.03.005
external_id:
  arxiv:
  - '1805.01652'
  isi:
  - '000430402700009'
fulldoi: https://doi.org/10.1016/j.crma.2018.03.005
intvolume: '       356'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1805.01652
month: '04'
oa: 1
oa_version: Preprint
page: 412-414
publication: Comptes Rendus Mathematique
publication_identifier:
  issn:
  - 1631-073X
publication_status: published
publisher: Elsevier
publist_id: '7420'
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the number of non-hexagons in a planar tiling
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 356
year: '2018'
...
---
_id: '2737'
abstract:
- lang: eng
  text: We derive the time-dependent Schrödinger–Poisson equation as the weak coupling
    limit of the N-body linear Schrödinger equation with Coulomb potential.
acknowledgement: "The authors thank the ESI in Vienna and the Austrian START project
  “Nonlinear Schrödinger\r\nand quantum Boltzmann equations” of N.J.M. for hospitality
  and support. Also, F.G. was supported by the Institut\r\nUniversitaire de France
  and N.J.M. by the bilateral Austrian-French “AMADEUS” programme. H.-T.Y. and L.E.
  were\r\nsupported by NSF Grants DMS-0072098 and DMS-9970323, respectively"
article_processing_charge: No
article_type: original
author:
- first_name: Claude
  full_name: Bardos, Claude
  last_name: Bardos
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
- first_name: François
  full_name: Golse, François
  last_name: Golse
- first_name: Norbert
  full_name: Mauser, Norbert
  last_name: Mauser
- first_name: Horng
  full_name: Yau, Horng
  last_name: Yau
citation:
  ama: Bardos C, Erdös L, Golse F, Mauser N, Yau H. Derivation of the Schrödinger-Poisson
    equation from the quantum N-body problem. <i>Comptes Rendus Mathematique</i>.
    2002;334(6):515-520. doi:<a href="https://doi.org/10.1016/S1631-073X(02)02253-7">10.1016/S1631-073X(02)02253-7</a>
  apa: Bardos, C., Erdös, L., Golse, F., Mauser, N., &#38; Yau, H. (2002). Derivation
    of the Schrödinger-Poisson equation from the quantum N-body problem. <i>Comptes
    Rendus Mathematique</i>. Elsevier. <a href="https://doi.org/10.1016/S1631-073X(02)02253-7">https://doi.org/10.1016/S1631-073X(02)02253-7</a>
  chicago: Bardos, Claude, László Erdös, François Golse, Norbert Mauser, and Horng
    Yau. “Derivation of the Schrödinger-Poisson Equation from the Quantum N-Body Problem.”
    <i>Comptes Rendus Mathematique</i>. Elsevier, 2002. <a href="https://doi.org/10.1016/S1631-073X(02)02253-7">https://doi.org/10.1016/S1631-073X(02)02253-7</a>.
  ieee: C. Bardos, L. Erdös, F. Golse, N. Mauser, and H. Yau, “Derivation of the Schrödinger-Poisson
    equation from the quantum N-body problem,” <i>Comptes Rendus Mathematique</i>,
    vol. 334, no. 6. Elsevier, pp. 515–520, 2002.
  ista: Bardos C, Erdös L, Golse F, Mauser N, Yau H. 2002. Derivation of the Schrödinger-Poisson
    equation from the quantum N-body problem. Comptes Rendus Mathematique. 334(6),
    515–520.
  mla: Bardos, Claude, et al. “Derivation of the Schrödinger-Poisson Equation from
    the Quantum N-Body Problem.” <i>Comptes Rendus Mathematique</i>, vol. 334, no.
    6, Elsevier, 2002, pp. 515–20, doi:<a href="https://doi.org/10.1016/S1631-073X(02)02253-7">10.1016/S1631-073X(02)02253-7</a>.
  short: C. Bardos, L. Erdös, F. Golse, N. Mauser, H. Yau, Comptes Rendus Mathematique
    334 (2002) 515–520.
date_created: 2018-12-11T11:59:20Z
date_published: 2002-03-30T00:00:00Z
date_updated: 2023-07-18T09:24:24Z
day: '30'
doi: 10.1016/S1631-073X(02)02253-7
extern: '1'
fulldoi: https://doi.org/10.1016/S1631-073X(02)02253-7
intvolume: '       334'
issue: '6'
language:
- iso: eng
month: '03'
oa_version: None
page: 515 - 520
publication: Comptes Rendus Mathematique
publication_identifier:
  issn:
  - 1631-073X
publication_status: published
publisher: Elsevier
publist_id: '4155'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Derivation of the Schrödinger-Poisson equation from the quantum N-body problem
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 334
year: '2002'
...