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Algebra and Discrete Mathematics, 2021, Volume 32, Issue 2, Pages 185–196
DOI: https://doi.org/10.12958/adm1912
(Mi adm814)
 

This article is cited in 3 scientific papers (total in 3 papers)

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
Full-text PDF (366 kB) Citations (3)
References:
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.
Received: 12.11.2021
Document Type: Article
MSC: 15B33, 15A30
Language: English
Citation: V. M. Bondarenko, M. Styopochkina, “On classifying the non-Tits $P$-critical posets”, Algebra Discrete Math., 32:2 (2021), 185–196
Citation in format AMSBIB
\Bibitem{BonSty21}
\by V.~M.~Bondarenko, M.~Styopochkina
\paper On classifying the non-Tits $P$-critical posets
\jour Algebra Discrete Math.
\yr 2021
\vol 32
\issue 2
\pages 185--196
\mathnet{http://mi.mathnet.ru/adm814}
\crossref{https://doi.org/10.12958/adm1912}
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  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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