Buchumschlag

On combinatorial properties of minimal posets with nonnegative Tits quadratic form

In this paper, we study combinatorial properties of finite posets connected with the negativity of their Tits quadratic form. We calculate the coefficients of transitivity for all minimal posets with nonnegative Tits quadratic form (such posets are called \(NP\)-critical and their number is 115 up t...

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Bibliographische Detailangaben
Datum:2026
1. Verfasser: Styopochkina, Maryna V.
Format: Artikel
Sprache:Englisch
Veröffentlicht: Lugansk National Taras Shevchenko University 2026
Schlagworte:
height
neighboring elements
Hasse diagram
Dynkin diagram
Tits quadratic form
\(NP\)-critical poset
coefficient of transitivity
06A07
11E04
Online Zugang:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2490
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Назва журналу:Algebra and Discrete Mathematics
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Algebra and Discrete Mathematics
Beschreibung
Zusammenfassung:In this paper, we study combinatorial properties of finite posets connected with the negativity of their Tits quadratic form. We calculate the coefficients of transitivity for all minimal posets with nonnegative Tits quadratic form (such posets are called \(NP\)-critical and their number is 115 up to isomorphism and duality). Some relationships between these coefficients and the heights of posets are established.
DOI:10.12958/adm2490

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