---
_id: '14660'
abstract:
- lang: eng
  text: "The classical Steinitz theorem states that if the origin belongs to the interior
    of the convex hull of a set \U0001D446⊂ℝ\U0001D451, then there are at most 2\U0001D451
    points of \U0001D446 whose convex hull contains the origin in the interior. Bárány,
    Katchalski,and Pach proved the following quantitative version of Steinitz’s theorem.
    Let \U0001D444 be a convex polytope in ℝ\U0001D451 containing the standard Euclidean
    unit ball \U0001D401\U0001D451. Then there exist at most 2\U0001D451 vertices
    of \U0001D444 whose convex hull \U0001D444′ satisfies \U0001D45F\U0001D401\U0001D451⊂\U0001D444′
    with \U0001D45F⩾\U0001D451−2\U0001D451. They conjectured that \U0001D45F⩾\U0001D450\U0001D451−1∕2
    holds with a universal constant \U0001D450>0. We prove \U0001D45F⩾15\U0001D4512,
    the first polynomial lower bound on \U0001D45F. Furthermore, we show that \U0001D45F
    is not greater than 2/√\U0001D451."
acknowledgement: M.N. was supported by the János Bolyai Scholarship of the Hungarian
  Academy of Sciences aswell as the National Research, Development and Innovation
  Fund (NRDI) grants K119670 andK131529, and the ÚNKP-22-5 New National Excellence
  Program of the Ministry for Innovationand Technology from the source of the NRDI
  as well as the ELTE TKP 2021-NKTA-62 fundingscheme
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Grigory
  full_name: Ivanov, Grigory
  id: 87744F66-5C6F-11EA-AFE0-D16B3DDC885E
  last_name: Ivanov
- first_name: Márton
  full_name: Naszódi, Márton
  last_name: Naszódi
citation:
  ama: 'Ivanov G, Naszódi M. Quantitative Steinitz theorem: A polynomial bound. <i>Bulletin
    of the London Mathematical Society</i>. 2023. doi:<a href="https://doi.org/10.1112/blms.12965">10.1112/blms.12965</a>'
  apa: 'Ivanov, G., &#38; Naszódi, M. (2023). Quantitative Steinitz theorem: A polynomial
    bound. <i>Bulletin of the London Mathematical Society</i>. London Mathematical
    Society. <a href="https://doi.org/10.1112/blms.12965">https://doi.org/10.1112/blms.12965</a>'
  chicago: 'Ivanov, Grigory, and Márton Naszódi. “Quantitative Steinitz Theorem: A
    Polynomial Bound.” <i>Bulletin of the London Mathematical Society</i>. London
    Mathematical Society, 2023. <a href="https://doi.org/10.1112/blms.12965">https://doi.org/10.1112/blms.12965</a>.'
  ieee: 'G. Ivanov and M. Naszódi, “Quantitative Steinitz theorem: A polynomial bound,”
    <i>Bulletin of the London Mathematical Society</i>. London Mathematical Society,
    2023.'
  ista: 'Ivanov G, Naszódi M. 2023. Quantitative Steinitz theorem: A polynomial bound.
    Bulletin of the London Mathematical Society.'
  mla: 'Ivanov, Grigory, and Márton Naszódi. “Quantitative Steinitz Theorem: A Polynomial
    Bound.” <i>Bulletin of the London Mathematical Society</i>, London Mathematical
    Society, 2023, doi:<a href="https://doi.org/10.1112/blms.12965">10.1112/blms.12965</a>.'
  short: G. Ivanov, M. Naszódi, Bulletin of the London Mathematical Society (2023).
date_created: 2023-12-10T23:00:58Z
date_published: 2023-12-04T00:00:00Z
date_updated: 2023-12-11T10:03:54Z
day: '04'
department:
- _id: UlWa
doi: 10.1112/blms.12965
external_id:
  arxiv:
  - '2212.04308'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: ' https://doi.org/10.1112/blms.12965'
month: '12'
oa: 1
oa_version: Published Version
publication: Bulletin of the London Mathematical Society
publication_identifier:
  eissn:
  - 1469-2120
  issn:
  - 0024-6093
publication_status: epub_ahead
publisher: London Mathematical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Quantitative Steinitz theorem: A polynomial bound'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...
---
_id: '11186'
abstract:
- lang: eng
  text: "In this note, we study large deviations of the number  \U0001D40D  of intercalates
    ( 2×2  combinatorial subsquares which are themselves Latin squares) in a random
    \ \U0001D45B×\U0001D45B  Latin square. In particular, for constant  \U0001D6FF>0
    \ we prove that  exp(−\U0001D442(\U0001D45B2log\U0001D45B))⩽Pr(\U0001D40D⩽(1−\U0001D6FF)\U0001D45B2/4)⩽exp(−Ω(\U0001D45B2))
    \ and  exp(−\U0001D442(\U0001D45B4/3(log\U0001D45B)))⩽Pr(\U0001D40D⩾(1+\U0001D6FF)\U0001D45B2/4)⩽exp(−Ω(\U0001D45B4/3(log\U0001D45B)2/3))
    . As a consequence, we deduce that a typical order- \U0001D45B  Latin square has
    \ (1+\U0001D45C(1))\U0001D45B2/4  intercalates, matching a lower bound due to
    Kwan and Sudakov and resolving an old conjecture of McKay and Wanless."
acknowledgement: "We thank Zach Hunter for pointing out some important typographical
  errors. We also thank the referee for several remarks which helped improve the paper
  substantially.\r\nKwan was supported by NSF grant DMS-1953990. Sah and Sawhney were
  supported by NSF Graduate Research Fellowship Program DGE-1745302."
article_processing_charge: No
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. Large deviations in random latin squares. <i>Bulletin
    of the London Mathematical Society</i>. 2022;54(4):1420-1438. doi:<a href="https://doi.org/10.1112/blms.12638">10.1112/blms.12638</a>
  apa: Kwan, M. A., Sah, A., &#38; Sawhney, M. (2022). Large deviations in random
    latin squares. <i>Bulletin of the London Mathematical Society</i>. Wiley. <a href="https://doi.org/10.1112/blms.12638">https://doi.org/10.1112/blms.12638</a>
  chicago: Kwan, Matthew Alan, Ashwin Sah, and Mehtaab Sawhney. “Large Deviations
    in Random Latin Squares.” <i>Bulletin of the London Mathematical Society</i>.
    Wiley, 2022. <a href="https://doi.org/10.1112/blms.12638">https://doi.org/10.1112/blms.12638</a>.
  ieee: M. A. Kwan, A. Sah, and M. Sawhney, “Large deviations in random latin squares,”
    <i>Bulletin of the London Mathematical Society</i>, vol. 54, no. 4. Wiley, pp.
    1420–1438, 2022.
  ista: Kwan MA, Sah A, Sawhney M. 2022. Large deviations in random latin squares.
    Bulletin of the London Mathematical Society. 54(4), 1420–1438.
  mla: Kwan, Matthew Alan, et al. “Large Deviations in Random Latin Squares.” <i>Bulletin
    of the London Mathematical Society</i>, vol. 54, no. 4, Wiley, 2022, pp. 1420–38,
    doi:<a href="https://doi.org/10.1112/blms.12638">10.1112/blms.12638</a>.
  short: M.A. Kwan, A. Sah, M. Sawhney, Bulletin of the London Mathematical Society
    54 (2022) 1420–1438.
date_created: 2022-04-17T22:01:48Z
date_published: 2022-08-01T00:00:00Z
date_updated: 2023-08-03T06:47:29Z
day: '01'
ddc:
- '510'
department:
- _id: MaKw
doi: 10.1112/blms.12638
external_id:
  arxiv:
  - '2106.11932'
  isi:
  - '000779920900001'
file:
- access_level: open_access
  checksum: 02d74e7ae955ba3c808e2a8aebe6ef98
  content_type: application/pdf
  creator: dernst
  date_created: 2023-02-03T09:43:38Z
  date_updated: 2023-02-03T09:43:38Z
  file_id: '12499'
  file_name: 2022_BulletinMathSociety_Kwan.pdf
  file_size: 233758
  relation: main_file
  success: 1
file_date_updated: 2023-02-03T09:43:38Z
has_accepted_license: '1'
intvolume: '        54'
isi: 1
issue: '4'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
page: 1420-1438
publication: Bulletin of the London Mathematical Society
publication_identifier:
  eissn:
  - 1469-2120
  issn:
  - 0024-6093
publication_status: published
publisher: Wiley
quality_controlled: '1'
scopus_import: '1'
status: public
title: Large deviations in random latin squares
tmp:
  image: /images/cc_by_nc.png
  legal_code_url: https://creativecommons.org/licenses/by-nc/4.0/legalcode
  name: Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)
  short: CC BY-NC (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 54
year: '2022'
...
---
_id: '6965'
abstract:
- lang: eng
  text: The central object of investigation of this paper is the Hirzebruch class,
    a deformation of the Todd class, given by Hirzebruch (for smooth varieties). The
    generalization for singular varieties is due to Brasselet–Schürmann–Yokura. Following
    the work of Weber, we investigate its equivariant version for (possibly singular)
    toric varieties. The local decomposition of the Hirzebruch class to the fixed
    points of the torus action and a formula for the local class in terms of the defining
    fan are recalled. After this review part, we prove the positivity of local Hirzebruch
    classes for all toric varieties, thus proving false the alleged counterexample
    given by Weber.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Kamil P
  full_name: Rychlewicz, Kamil P
  id: 85A07246-A8BF-11E9-B4FA-D9E3E5697425
  last_name: Rychlewicz
citation:
  ama: Rychlewicz KP. The positivity of local equivariant Hirzebruch class for toric
    varieties. <i>Bulletin of the London Mathematical Society</i>. 2021;53(2):560-574.
    doi:<a href="https://doi.org/10.1112/blms.12442">10.1112/blms.12442</a>
  apa: Rychlewicz, K. P. (2021). The positivity of local equivariant Hirzebruch class
    for toric varieties. <i>Bulletin of the London Mathematical Society</i>. Wiley.
    <a href="https://doi.org/10.1112/blms.12442">https://doi.org/10.1112/blms.12442</a>
  chicago: Rychlewicz, Kamil P. “The Positivity of Local Equivariant Hirzebruch Class
    for Toric Varieties.” <i>Bulletin of the London Mathematical Society</i>. Wiley,
    2021. <a href="https://doi.org/10.1112/blms.12442">https://doi.org/10.1112/blms.12442</a>.
  ieee: K. P. Rychlewicz, “The positivity of local equivariant Hirzebruch class for
    toric varieties,” <i>Bulletin of the London Mathematical Society</i>, vol. 53,
    no. 2. Wiley, pp. 560–574, 2021.
  ista: Rychlewicz KP. 2021. The positivity of local equivariant Hirzebruch class
    for toric varieties. Bulletin of the London Mathematical Society. 53(2), 560–574.
  mla: Rychlewicz, Kamil P. “The Positivity of Local Equivariant Hirzebruch Class
    for Toric Varieties.” <i>Bulletin of the London Mathematical Society</i>, vol.
    53, no. 2, Wiley, 2021, pp. 560–74, doi:<a href="https://doi.org/10.1112/blms.12442">10.1112/blms.12442</a>.
  short: K.P. Rychlewicz, Bulletin of the London Mathematical Society 53 (2021) 560–574.
date_created: 2019-10-24T08:04:09Z
date_published: 2021-04-01T00:00:00Z
date_updated: 2023-08-04T10:43:39Z
day: '01'
department:
- _id: TaHa
doi: 10.1112/blms.12442
external_id:
  arxiv:
  - '1910.10435'
  isi:
  - '000594805800001'
intvolume: '        53'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1910.10435
month: '04'
oa: 1
oa_version: Preprint
page: 560-574
publication: Bulletin of the London Mathematical Society
publication_identifier:
  eissn:
  - 1469-2120
  issn:
  - 0024-6093
publication_status: published
publisher: Wiley
quality_controlled: '1'
scopus_import: '1'
status: public
title: The positivity of local equivariant Hirzebruch class for toric varieties
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 53
year: '2021'
...
---
_id: '9572'
abstract:
- lang: eng
  text: We prove that every n-vertex tournament G has an acyclic subgraph with chromatic
    number at least n5/9−o(1), while there exists an n-vertex tournament G whose every
    acyclic subgraph has chromatic number at most n3/4+o(1). This establishes in a
    strong form a conjecture of Nassar and Yuster and improves on another result of
    theirs. Our proof combines probabilistic and spectral techniques together with
    some additional ideas. In particular, we prove a lemma showing that every tournament
    with many transitive subtournaments has a large subtournament that is almost transitive.
    This may be of independent interest.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Jacob
  full_name: Fox, Jacob
  last_name: Fox
- 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: Benny
  full_name: Sudakov, Benny
  last_name: Sudakov
citation:
  ama: Fox J, Kwan MA, Sudakov B. Acyclic subgraphs of tournaments with high chromatic
    number. <i>Bulletin of the London Mathematical Society</i>. 2021;53(2):619-630.
    doi:<a href="https://doi.org/10.1112/blms.12446">10.1112/blms.12446</a>
  apa: Fox, J., Kwan, M. A., &#38; Sudakov, B. (2021). Acyclic subgraphs of tournaments
    with high chromatic number. <i>Bulletin of the London Mathematical Society</i>.
    Wiley. <a href="https://doi.org/10.1112/blms.12446">https://doi.org/10.1112/blms.12446</a>
  chicago: Fox, Jacob, Matthew Alan Kwan, and Benny Sudakov. “Acyclic Subgraphs of
    Tournaments with High Chromatic Number.” <i>Bulletin of the London Mathematical
    Society</i>. Wiley, 2021. <a href="https://doi.org/10.1112/blms.12446">https://doi.org/10.1112/blms.12446</a>.
  ieee: J. Fox, M. A. Kwan, and B. Sudakov, “Acyclic subgraphs of tournaments with
    high chromatic number,” <i>Bulletin of the London Mathematical Society</i>, vol.
    53, no. 2. Wiley, pp. 619–630, 2021.
  ista: Fox J, Kwan MA, Sudakov B. 2021. Acyclic subgraphs of tournaments with high
    chromatic number. Bulletin of the London Mathematical Society. 53(2), 619–630.
  mla: Fox, Jacob, et al. “Acyclic Subgraphs of Tournaments with High Chromatic Number.”
    <i>Bulletin of the London Mathematical Society</i>, vol. 53, no. 2, Wiley, 2021,
    pp. 619–30, doi:<a href="https://doi.org/10.1112/blms.12446">10.1112/blms.12446</a>.
  short: J. Fox, M.A. Kwan, B. Sudakov, Bulletin of the London Mathematical Society
    53 (2021) 619–630.
date_created: 2021-06-21T06:11:56Z
date_published: 2021-04-03T00:00:00Z
date_updated: 2023-02-23T14:01:21Z
day: '03'
doi: 10.1112/blms.12446
extern: '1'
external_id:
  arxiv:
  - '1912.07722'
intvolume: '        53'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1912.07722
month: '04'
oa: 1
oa_version: Preprint
page: 619-630
publication: Bulletin of the London Mathematical Society
publication_identifier:
  eissn:
  - 1469-2120
  issn:
  - 0024-6093
publication_status: published
publisher: Wiley
quality_controlled: '1'
scopus_import: '1'
status: public
title: Acyclic subgraphs of tournaments with high chromatic number
type: journal_article
user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf
volume: 53
year: '2021'
...
---
_id: '9573'
abstract:
- lang: eng
  text: It is a classical fact that for any ε>0, a random permutation of length n=(1+ε)k2/4
    typically contains a monotone subsequence of length k. As a far-reaching generalization,
    Alon conjectured that a random permutation of this same length n is typically
    k-universal, meaning that it simultaneously contains every pattern of length k.
    He also made the simple observation that for n=O(k2logk), a random length-n permutation
    is typically k-universal. We make the first significant progress towards Alon's
    conjecture by showing that n=2000k2loglogk suffices.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Xiaoyu
  full_name: He, Xiaoyu
  last_name: He
- first_name: Matthew Alan
  full_name: Kwan, Matthew Alan
  id: 5fca0887-a1db-11eb-95d1-ca9d5e0453b3
  last_name: Kwan
  orcid: 0000-0002-4003-7567
citation:
  ama: He X, Kwan MA. Universality of random permutations. <i>Bulletin of the London
    Mathematical Society</i>. 2020;52(3):515-529. doi:<a href="https://doi.org/10.1112/blms.12345">10.1112/blms.12345</a>
  apa: He, X., &#38; Kwan, M. A. (2020). Universality of random permutations. <i>Bulletin
    of the London Mathematical Society</i>. Wiley. <a href="https://doi.org/10.1112/blms.12345">https://doi.org/10.1112/blms.12345</a>
  chicago: He, Xiaoyu, and Matthew Alan Kwan. “Universality of Random Permutations.”
    <i>Bulletin of the London Mathematical Society</i>. Wiley, 2020. <a href="https://doi.org/10.1112/blms.12345">https://doi.org/10.1112/blms.12345</a>.
  ieee: X. He and M. A. Kwan, “Universality of random permutations,” <i>Bulletin of
    the London Mathematical Society</i>, vol. 52, no. 3. Wiley, pp. 515–529, 2020.
  ista: He X, Kwan MA. 2020. Universality of random permutations. Bulletin of the
    London Mathematical Society. 52(3), 515–529.
  mla: He, Xiaoyu, and Matthew Alan Kwan. “Universality of Random Permutations.” <i>Bulletin
    of the London Mathematical Society</i>, vol. 52, no. 3, Wiley, 2020, pp. 515–29,
    doi:<a href="https://doi.org/10.1112/blms.12345">10.1112/blms.12345</a>.
  short: X. He, M.A. Kwan, Bulletin of the London Mathematical Society 52 (2020) 515–529.
date_created: 2021-06-21T06:23:42Z
date_published: 2020-06-01T00:00:00Z
date_updated: 2023-02-23T14:01:23Z
day: '01'
doi: 10.1112/blms.12345
extern: '1'
external_id:
  arxiv:
  - '1911.12878'
intvolume: '        52'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1911.12878
month: '06'
oa: 1
oa_version: Preprint
page: 515-529
publication: Bulletin of the London Mathematical Society
publication_identifier:
  eissn:
  - 1469-2120
  issn:
  - 0024-6093
publication_status: published
publisher: Wiley
quality_controlled: '1'
scopus_import: '1'
status: public
title: Universality of random permutations
type: journal_article
user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf
volume: 52
year: '2020'
...