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Эта публикация цитируется в 3 научных статьях (всего в 3 статьях)
RESEARCH ARTICLE
On classifying the non-Tits $P$-critical posets
V. M. Bondarenkoa, M. Styopochkinab a Institute of Mathematics, Tereshchenkivska str., 3, 01024 Kyiv, Ukraine
b Polissia National University, Staryi Boulevard, 7, 10008 Zhytomyr, Ukraine
Аннотация:
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.
Ключевые слова:
Hasse diagram, Kleiner's poset, minimax equivalence, quadratic Tits form, $0$-balanced subposet, $P$-critical poset, Tits $P$-critical poset.
Поступила в редакцию: 12.11.2021
Образец цитирования:
V. M. Bondarenko, M. Styopochkina, “On classifying the non-Tits $P$-critical posets”, Algebra Discrete Math., 32:2 (2021), 185–196
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/adm814 https://www.mathnet.ru/rus/adm/v32/i2/p185
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