On classifying the non-Tits \(P\)-critical posets

• Date: 2022
• Main Authors: Bondarenko, V. M., Styopochkina, M. V.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2022
• Subjects: Hasse diagram; Kleiner's poset; minimax equivalence; quadratic Tits form; \(0\)-balanced subposet; \(P\)-critical poset; Tits \(P\)-critical poset; 15B33; 15A30
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1912
• Journal Title: Algebra and Discrete Mathematics

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...