On classifying the non-Tits \(P\)-critical posets
In 2005, the authors described all introduced by them \(P\)-critical posets (minimal finite posets with the quadratic Tits form not being positive); up to isomorphism, their number is 132 (75 if duality is considered). Later (in 2014) A. Polak and D. Simson offered an alternative way of proving by u...
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| Дата: | 2022 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2022
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1912 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| _version_ | 1856543296264863744 |
|---|---|
| author | Bondarenko, V. M. Styopochkina, M. V. |
| author_facet | Bondarenko, V. M. Styopochkina, M. V. |
| author_sort | Bondarenko, V. M. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2022-04-15T07:11:32Z |
| description | In 2005, the authors described all introduced by them \(P\)-critical posets (minimal finite posets with the quadratic Tits form not being positive); up to isomorphism, their number is 132 (75 if duality is considered). Later (in 2014) A. Polak and D. Simson offered an alternative way of proving by using computer algebra tools. In doing this, they defined and described the Tits \(P\)-critical posets as a special case of the \(P\)-critical posets. In this paper we classify all the non-Tits \(P\)-critical posets without complex calculations and without using the list of all \(P\)-critical ones. |
| first_indexed | 2025-12-02T15:25:57Z |
| format | Article |
| id | admjournalluguniveduua-article-1912 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:25:57Z |
| publishDate | 2022 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-19122022-04-15T07:11:32Z On classifying the non-Tits \(P\)-critical posets Bondarenko, V. M. Styopochkina, M. V. Hasse diagram, Kleiner's poset, minimax equivalence, quadratic Tits form, \(0\)-balanced subposet, \(P\)-critical poset, Tits \(P\)-critical poset 15B33, 15A30 In 2005, the authors described all introduced by them \(P\)-critical posets (minimal finite posets with the quadratic Tits form not being positive); up to isomorphism, their number is 132 (75 if duality is considered). Later (in 2014) A. Polak and D. Simson offered an alternative way of proving by using computer algebra tools. In doing this, they defined and described the Tits \(P\)-critical posets as a special case of the \(P\)-critical posets. In this paper we classify all the non-Tits \(P\)-critical posets without complex calculations and without using the list of all \(P\)-critical ones. Lugansk National Taras Shevchenko University 2022-03-28 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1912 10.12958/adm1912 Algebra and Discrete Mathematics; Vol 32, No 2 (2021) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1912/pdf Copyright (c) 2022 Algebra and Discrete Mathematics |
| spellingShingle | Hasse diagram Kleiner's poset minimax equivalence quadratic Tits form \(0\)-balanced subposet \(P\)-critical poset Tits \(P\)-critical poset 15B33 15A30 Bondarenko, V. M. Styopochkina, M. V. On classifying the non-Tits \(P\)-critical posets |
| title | On classifying the non-Tits \(P\)-critical posets |
| title_full | On classifying the non-Tits \(P\)-critical posets |
| title_fullStr | On classifying the non-Tits \(P\)-critical posets |
| title_full_unstemmed | On classifying the non-Tits \(P\)-critical posets |
| title_short | On classifying the non-Tits \(P\)-critical posets |
| title_sort | on classifying the non-tits \(p\)-critical posets |
| topic | Hasse diagram Kleiner's poset minimax equivalence quadratic Tits form \(0\)-balanced subposet \(P\)-critical poset Tits \(P\)-critical poset 15B33 15A30 |
| topic_facet | Hasse diagram Kleiner's poset minimax equivalence quadratic Tits form \(0\)-balanced subposet \(P\)-critical poset Tits \(P\)-critical poset 15B33 15A30 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1912 |
| work_keys_str_mv | AT bondarenkovm onclassifyingthenontitspcriticalposets AT styopochkinamv onclassifyingthenontitspcriticalposets |