On classifying the non-Tits \(P\)-critical posets

On classifying the non-Tits \(P\)-critical posets

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 u...

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Datum:2022
Hauptverfasser: Bondarenko, V. M., Styopochkina, M. V.
Format: Artikel
Sprache:English
Veröffentlicht: Lugansk National Taras Shevchenko University 2022
Schlagworte:
Hasse diagram
Kleiner's poset
minimax equivalence
quadratic Tits form
\(0\)-balanced subposet
\(P\)-critical poset
Tits \(P\)-critical poset
15B33
15A30
Online Zugang:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1912
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Назва журналу:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics
Beschreibung
Zusammenfassung: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.

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