Geodesic
On classifying the non-Tits $P$-critical posets
Algebra and discrete mathematics, Tome 32 (2021) no. 2, pp. 185-196

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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: Kleiner's poset, minimax equivalence, $0$-balanced subposet, $P$-critical poset, Tits $P$-critical poset.
Mots-clés : Hasse diagram, quadratic Tits form 
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     title = {On classifying the {non-Tits} $P$-critical posets},
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V. M. Bondarenko; M. Styopochkina. On classifying the non-Tits $P$-critical posets. Algebra and discrete mathematics, Tome 32 (2021) no. 2, pp. 185-196. http://geodesic.mathdoc.fr/item/ADM_2021_32_2_a1/