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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| Date: | 2022 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2022
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1912 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Summary: | 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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