[{"ddc":["510","516"],"abstract":[{"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","lang":"eng"}],"day":"31","degree_awarded":"MS","doi":"10.15479/at:ista:13331","year":"2023","citation":{"ista":"Köse S. 2023. Exterior algebra and combinatorics. Institute of Science and Technology Austria.","short":"S. Köse, Exterior Algebra and Combinatorics, Institute of Science and Technology Austria, 2023.","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>.","ieee":"S. Köse, “Exterior algebra and combinatorics,” Institute of Science and Technology Austria, 2023.","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>.","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>"},"date_updated":"2023-10-04T11:54:56Z","publisher":"Institute of Science and Technology Austria","file_date_updated":"2023-08-03T15:28:55Z","page":"26","title":"Exterior algebra and combinatorics","alternative_title":["ISTA Master's Thesis"],"department":[{"_id":"GradSch"},{"_id":"UlWa"}],"article_processing_charge":"No","date_created":"2023-07-31T10:20:55Z","publication_status":"published","author":[{"first_name":"Seyda","last_name":"Köse","full_name":"Köse, Seyda","id":"8ba3170d-dc85-11ea-9058-c4251c96a6eb"}],"_id":"13331","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","related_material":{"record":[{"status":"public","id":"12680","relation":"part_of_dissertation"}]},"status":"public","file":[{"creator":"skoese","file_id":"13333","relation":"source_file","access_level":"closed","file_name":"Exterior Algebra and Combinatorics.zip","content_type":"application/x-zip-compressed","date_updated":"2023-07-31T10:16:32Z","checksum":"96ee518d796d02af71395622c45de03c","file_size":28684,"date_created":"2023-07-31T10:16:32Z"},{"success":1,"relation":"main_file","access_level":"open_access","creator":"skoese","file_id":"13480","file_size":4953418,"checksum":"f610f4713f88bc477de576aaa46b114e","date_created":"2023-08-03T15:28:55Z","file_name":"thesis-pdfa.pdf","content_type":"application/pdf","date_updated":"2023-08-03T15:28:55Z"}],"oa":1,"supervisor":[{"id":"36690CA2-F248-11E8-B48F-1D18A9856A87","first_name":"Uli","last_name":"Wagner","orcid":"0000-0002-1494-0568","full_name":"Wagner, Uli"}],"publication_identifier":{"issn":["2791-4585"]},"type":"dissertation","date_published":"2023-07-31T00:00:00Z","language":[{"iso":"eng"}],"month":"07","oa_version":"Published Version","has_accepted_license":"1"},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","related_material":{"record":[{"status":"public","id":"13331","relation":"dissertation_contains"}]},"status":"public","main_file_link":[{"url":" https://doi.org/10.48550/arXiv.2201.10892","open_access":"1"}],"oa":1,"publication_identifier":{"issn":["0012-365X"]},"date_published":"2023-06-01T00:00:00Z","type":"journal_article","language":[{"iso":"eng"}],"month":"06","article_number":"113363","oa_version":"Preprint","publication":"Discrete Mathematics","volume":346,"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."}],"doi":"10.1016/j.disc.2023.113363","arxiv":1,"day":"01","external_id":{"arxiv":["2201.10892"]},"date_updated":"2023-10-04T11:54:57Z","citation":{"short":"G. Ivanov, S. Köse, Discrete Mathematics 346 (2023).","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>.","ista":"Ivanov G, Köse S. 2023. Erdős-Ko-Rado and Hilton-Milner theorems for two-forms. Discrete Mathematics. 346(6), 113363.","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>","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>","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."},"year":"2023","article_type":"letter_note","publisher":"Elsevier","quality_controlled":"1","title":"Erdős-Ko-Rado and Hilton-Milner theorems for two-forms","intvolume":"       346","publication_status":"published","article_processing_charge":"No","date_created":"2023-02-26T23:01:00Z","department":[{"_id":"UlWa"},{"_id":"GradSch"}],"author":[{"id":"87744F66-5C6F-11EA-AFE0-D16B3DDC885E","full_name":"Ivanov, Grigory","first_name":"Grigory","last_name":"Ivanov"},{"full_name":"Köse, Seyda","first_name":"Seyda","last_name":"Köse","id":"8ba3170d-dc85-11ea-9058-c4251c96a6eb"}],"issue":"6","_id":"12680","scopus_import":"1"},{"external_id":{"isi":["000766422000002"]},"isi":1,"citation":{"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.","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.","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>","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.","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>."},"year":"2022","date_updated":"2023-09-05T15:35:55Z","abstract":[{"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.","lang":"eng"}],"day":"01","doi":"10.1007/s12095-022-00557-8","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.","volume":14,"issue":"4","author":[{"full_name":"Köse, Seyda","first_name":"Seyda","last_name":"Köse","id":"8ba3170d-dc85-11ea-9058-c4251c96a6eb"},{"full_name":"Özbudak, Ferruh","last_name":"Özbudak","first_name":"Ferruh"}],"scopus_import":"1","_id":"10842","intvolume":"        14","title":"Factorization of some polynomials over finite local commutative rings and applications to certain self-dual and LCD codes","department":[{"_id":"GradSch"}],"article_processing_charge":"No","date_created":"2022-03-10T12:16:19Z","publication_status":"published","quality_controlled":"1","page":"933-948","article_type":"original","publisher":"Springer Nature","type":"journal_article","date_published":"2022-07-01T00:00:00Z","publication_identifier":{"issn":["1936-2447"],"eissn":["1936-2455"]},"status":"public","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","publication":"Cryptography and Communications","month":"07","oa_version":"None","keyword":["Applied Mathematics","Computational Theory and Mathematics","Computer Networks and Communications"],"language":[{"iso":"eng"}]}]