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...
Збережено в:
| Дата: | 2022 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2022
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| Теми: | |
| 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| Резюме: | 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. |
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