Author:
Bondarenko V. M., ,Styopochkina M. V.,
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.
Publisher
Luhansk Taras Shevchenko National University
Subject
Discrete Mathematics and Combinatorics,Algebra and Number Theory
Reference20 articles.
1. [1] P. Gabriel,Unzerlegbare Darstellungen, Manuscripta Math.,6(1972), pp. 71-103.
2. [2]L. A. Nazarova, A. V. Roiter,Representations of partially ordered sets, Zap. Nauch.Semin. LOMI,28(1972), pp. 5-31 (in Russian)
3. English trans. J. Soviet math.,3 (1975), pp. 585-606.
4. [3]D. Simson,Linear representations of partially ordered sets and vector space cate-gories,Gordon and Breach, Philadelphia, 1992.
5. [4]Ju. A. Drozd,Coxeter transformations and representations of partially ordered sets,Funkcional. Anal. i Prilozen.,8, No 3 (1974), pp. 34Ð42 (in Russian)
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献