---
_id: '13331'
abstract:
- lang: eng
  text: "The extension of extremal combinatorics to the setting of exterior algebra
    is a work\r\nin progress that gained attention recently. In this thesis, we study
    the combinatorial structure of exterior algebra by introducing a dictionary that
    translates the notions from the set systems into the framework of exterior algebra.
    We show both generalizations of celebrated Erdös--Ko--Rado theorem and Hilton--Milner
    theorem to the setting of exterior algebra in the simplest non-trivial case of
    two-forms.\r\n"
alternative_title:
- ISTA Master's Thesis
article_processing_charge: No
author:
- first_name: Seyda
  full_name: Köse, Seyda
  id: 8ba3170d-dc85-11ea-9058-c4251c96a6eb
  last_name: Köse
citation:
  ama: Köse S. Exterior algebra and combinatorics. 2023. doi:<a href="https://doi.org/10.15479/at:ista:13331">10.15479/at:ista:13331</a>
  apa: Köse, S. (2023). <i>Exterior algebra and combinatorics</i>. Institute of Science
    and Technology Austria. <a href="https://doi.org/10.15479/at:ista:13331">https://doi.org/10.15479/at:ista:13331</a>
  chicago: Köse, Seyda. “Exterior Algebra and Combinatorics.” Institute of Science
    and Technology Austria, 2023. <a href="https://doi.org/10.15479/at:ista:13331">https://doi.org/10.15479/at:ista:13331</a>.
  ieee: S. Köse, “Exterior algebra and combinatorics,” Institute of Science and Technology
    Austria, 2023.
  ista: Köse S. 2023. Exterior algebra and combinatorics. Institute of Science and
    Technology Austria.
  mla: Köse, Seyda. <i>Exterior Algebra and Combinatorics</i>. Institute of Science
    and Technology Austria, 2023, doi:<a href="https://doi.org/10.15479/at:ista:13331">10.15479/at:ista:13331</a>.
  short: S. Köse, Exterior Algebra and Combinatorics, Institute of Science and Technology
    Austria, 2023.
date_created: 2023-07-31T10:20:55Z
date_published: 2023-07-31T00:00:00Z
date_updated: 2023-10-04T11:54:56Z
day: '31'
ddc:
- '510'
- '516'
degree_awarded: MS
department:
- _id: GradSch
- _id: UlWa
doi: 10.15479/at:ista:13331
file:
- access_level: closed
  checksum: 96ee518d796d02af71395622c45de03c
  content_type: application/x-zip-compressed
  creator: skoese
  date_created: 2023-07-31T10:16:32Z
  date_updated: 2023-07-31T10:16:32Z
  file_id: '13333'
  file_name: Exterior Algebra and Combinatorics.zip
  file_size: 28684
  relation: source_file
- access_level: open_access
  checksum: f610f4713f88bc477de576aaa46b114e
  content_type: application/pdf
  creator: skoese
  date_created: 2023-08-03T15:28:55Z
  date_updated: 2023-08-03T15:28:55Z
  file_id: '13480'
  file_name: thesis-pdfa.pdf
  file_size: 4953418
  relation: main_file
  success: 1
file_date_updated: 2023-08-03T15:28:55Z
has_accepted_license: '1'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
page: '26'
publication_identifier:
  issn:
  - 2791-4585
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
  record:
  - id: '12680'
    relation: part_of_dissertation
    status: public
status: public
supervisor:
- first_name: Uli
  full_name: Wagner, Uli
  id: 36690CA2-F248-11E8-B48F-1D18A9856A87
  last_name: Wagner
  orcid: 0000-0002-1494-0568
title: Exterior algebra and combinatorics
type: dissertation
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2023'
...
---
_id: '12680'
abstract:
- lang: eng
  text: The celebrated Erdős–Ko–Rado theorem about the maximal size of an intersecting
    family of r-element subsets of  was extended to the setting of exterior algebra
    in [5, Theorem 2.3] and in [6, Theorem 1.4]. However, the equality case has not
    been settled yet. In this short note, we show that the extension of the Erdős–Ko–Rado
    theorem and the characterization of the equality case therein, as well as those
    of the Hilton–Milner theorem to the setting of exterior algebra in the simplest
    non-trivial case of two-forms follow from a folklore puzzle about possible arrangements
    of an intersecting family of lines.
article_number: '113363'
article_processing_charge: No
article_type: letter_note
arxiv: 1
author:
- first_name: Grigory
  full_name: Ivanov, Grigory
  id: 87744F66-5C6F-11EA-AFE0-D16B3DDC885E
  last_name: Ivanov
- first_name: Seyda
  full_name: Köse, Seyda
  id: 8ba3170d-dc85-11ea-9058-c4251c96a6eb
  last_name: Köse
citation:
  ama: Ivanov G, Köse S. Erdős-Ko-Rado and Hilton-Milner theorems for two-forms. <i>Discrete
    Mathematics</i>. 2023;346(6). doi:<a href="https://doi.org/10.1016/j.disc.2023.113363">10.1016/j.disc.2023.113363</a>
  apa: Ivanov, G., &#38; Köse, S. (2023). Erdős-Ko-Rado and Hilton-Milner theorems
    for two-forms. <i>Discrete Mathematics</i>. Elsevier. <a href="https://doi.org/10.1016/j.disc.2023.113363">https://doi.org/10.1016/j.disc.2023.113363</a>
  chicago: Ivanov, Grigory, and Seyda Köse. “Erdős-Ko-Rado and Hilton-Milner Theorems
    for Two-Forms.” <i>Discrete Mathematics</i>. Elsevier, 2023. <a href="https://doi.org/10.1016/j.disc.2023.113363">https://doi.org/10.1016/j.disc.2023.113363</a>.
  ieee: G. Ivanov and S. Köse, “Erdős-Ko-Rado and Hilton-Milner theorems for two-forms,”
    <i>Discrete Mathematics</i>, vol. 346, no. 6. Elsevier, 2023.
  ista: Ivanov G, Köse S. 2023. Erdős-Ko-Rado and Hilton-Milner theorems for two-forms.
    Discrete Mathematics. 346(6), 113363.
  mla: Ivanov, Grigory, and Seyda Köse. “Erdős-Ko-Rado and Hilton-Milner Theorems
    for Two-Forms.” <i>Discrete Mathematics</i>, vol. 346, no. 6, 113363, Elsevier,
    2023, doi:<a href="https://doi.org/10.1016/j.disc.2023.113363">10.1016/j.disc.2023.113363</a>.
  short: G. Ivanov, S. Köse, Discrete Mathematics 346 (2023).
date_created: 2023-02-26T23:01:00Z
date_published: 2023-06-01T00:00:00Z
date_updated: 2023-10-04T11:54:57Z
day: '01'
department:
- _id: UlWa
- _id: GradSch
doi: 10.1016/j.disc.2023.113363
external_id:
  arxiv:
  - '2201.10892'
intvolume: '       346'
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: ' https://doi.org/10.48550/arXiv.2201.10892'
month: '06'
oa: 1
oa_version: Preprint
publication: Discrete Mathematics
publication_identifier:
  issn:
  - 0012-365X
publication_status: published
publisher: Elsevier
quality_controlled: '1'
related_material:
  record:
  - id: '13331'
    relation: dissertation_contains
    status: public
scopus_import: '1'
status: public
title: Erdős-Ko-Rado and Hilton-Milner theorems for two-forms
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 346
year: '2023'
...
---
_id: '10842'
abstract:
- lang: eng
  text: We determine the unique factorization of some polynomials over a finite local
    commutative ring with identity explicitly. This solves and generalizes the main
    conjecture of Qian, Shi and Solé in [13]. We also give some applications to enumeration
    of certain generalized double circulant self-dual and linear complementary dual
    (LCD) codes over some finite rings together with an application in asymptotic
    coding theory.
acknowledgement: The authors would like to thank Prof. Dr. Minjia Shi for bringing
  [13, Conjecture 3.5] to our attention. We would also like to thank the associate
  editor and anonymous reviewers for their valuable comments and suggestions which
  improved and clarified the manuscript.
article_processing_charge: No
article_type: original
author:
- first_name: Seyda
  full_name: Köse, Seyda
  id: 8ba3170d-dc85-11ea-9058-c4251c96a6eb
  last_name: Köse
- first_name: Ferruh
  full_name: Özbudak, Ferruh
  last_name: Özbudak
citation:
  ama: Köse S, Özbudak F. Factorization of some polynomials over finite local commutative
    rings and applications to certain self-dual and LCD codes. <i>Cryptography and
    Communications</i>. 2022;14(4):933-948. doi:<a href="https://doi.org/10.1007/s12095-022-00557-8">10.1007/s12095-022-00557-8</a>
  apa: Köse, S., &#38; Özbudak, F. (2022). Factorization of some polynomials over
    finite local commutative rings and applications to certain self-dual and LCD codes.
    <i>Cryptography and Communications</i>. Springer Nature. <a href="https://doi.org/10.1007/s12095-022-00557-8">https://doi.org/10.1007/s12095-022-00557-8</a>
  chicago: Köse, Seyda, and Ferruh Özbudak. “Factorization of Some Polynomials over
    Finite Local Commutative Rings and Applications to Certain Self-Dual and LCD Codes.”
    <i>Cryptography and Communications</i>. Springer Nature, 2022. <a href="https://doi.org/10.1007/s12095-022-00557-8">https://doi.org/10.1007/s12095-022-00557-8</a>.
  ieee: S. Köse and F. Özbudak, “Factorization of some polynomials over finite local
    commutative rings and applications to certain self-dual and LCD codes,” <i>Cryptography
    and Communications</i>, vol. 14, no. 4. Springer Nature, pp. 933–948, 2022.
  ista: Köse S, Özbudak F. 2022. Factorization of some polynomials over finite local
    commutative rings and applications to certain self-dual and LCD codes. Cryptography
    and Communications. 14(4), 933–948.
  mla: Köse, Seyda, and Ferruh Özbudak. “Factorization of Some Polynomials over Finite
    Local Commutative Rings and Applications to Certain Self-Dual and LCD Codes.”
    <i>Cryptography and Communications</i>, vol. 14, no. 4, Springer Nature, 2022,
    pp. 933–48, doi:<a href="https://doi.org/10.1007/s12095-022-00557-8">10.1007/s12095-022-00557-8</a>.
  short: S. Köse, F. Özbudak, Cryptography and Communications 14 (2022) 933–948.
date_created: 2022-03-10T12:16:19Z
date_published: 2022-07-01T00:00:00Z
date_updated: 2023-09-05T15:35:55Z
day: '01'
department:
- _id: GradSch
doi: 10.1007/s12095-022-00557-8
external_id:
  isi:
  - '000766422000002'
intvolume: '        14'
isi: 1
issue: '4'
keyword:
- Applied Mathematics
- Computational Theory and Mathematics
- Computer Networks and Communications
language:
- iso: eng
month: '07'
oa_version: None
page: 933-948
publication: Cryptography and Communications
publication_identifier:
  eissn:
  - 1936-2455
  issn:
  - 1936-2447
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Factorization of some polynomials over finite local commutative rings and applications
  to certain self-dual and LCD codes
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 14
year: '2022'
...