On combinatorial properties of minimal posets with nonnegative Tits quadratic form

• Date: 2026
• Main Author: Styopochkina, Maryna V.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2026
• Subjects: height; neighboring elements; Hasse diagram; Dynkin diagram; Tits quadratic form; \(NP\)-critical poset; coefficient of transitivity; 06A07; 11E04
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2490
• Journal Title: Algebra and Discrete Mathematics

In this paper, we study combinatorial properties of finite posets connected with the negativity of their Tits quadratic form. We calculate the coefficients of transitivity for all minimal posets with nonnegative Tits quadratic form (such posets are called \(NP\)-critical and their number is 115 up t...