This article is cited in 4 papers

RESEARCH ARTICLE

On classifying the non-Tits $P$-critical posets

V. M. Bondarenko^a, M. Styopochkina<sup>b

a</sup> Institute of Mathematics, Tereshchenkivska str., 3, 01024 Kyiv, Ukraine
^b Polissia National University, Staryi Boulevard, 7, 10008 Zhytomyr, Ukraine

Abstract: 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.

Keywords: Hasse diagram, Kleiner's poset, minimax equivalence, quadratic Tits form, $0$-balanced subposet, $P$-critical poset, Tits $P$-critical poset.

MSC: 15B33, 15A30

Received: 12.11.2021

Language: English

DOI: 10.12958/adm1912