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ЖУРНАЛЫ // Algebra and Discrete Mathematics // Архив

Algebra Discrete Math., 2019, том 27, выпуск 2, страницы 202–211 (Mi adm703)

RESEARCH ARTICLE

The classification of serial posets with the non-negative quadratic Tits form being principal

Vitalij M. Bondarenkoa, Marina V. Styopochkinab

a Institute of Mathematics, Tereshchenkivska str., 3, 01024 Kyiv, Ukraine
b Zhytomyr National Agroecological Univ., Staryi Boulevard, 7, 10008 Zhytomyr, Ukraine

Аннотация: Using (introduced by the first author) the method of (min, max)-equivalence, we classify all serial principal posets, i.e. the posets $S$ satisfying the following conditions: (1) the quadratic Tits form $q_S(z)\colon\mathbb{Z}^{|S|+1}\to\mathbb{Z}$ of $S$ is non-negative; (2) $\operatorname{Ker}q_S(z):=\{t\mid q_S(t)=0\}$ is an infinite cyclic group (equivalently, the corank of the symmetric matrix of $q_S(z)$ is equal to $1$); (3) for any $m\in\mathbb{N}$, there is a poset $S(m)\supset S$ such that $S(m)$ satisfies (1), (2) and $|S(m)\setminus S|=m$.

Ключевые слова: quiver, serial poset, principal poset, quadratic Tits form, semichain, minimax equivalence, one-side and two-side sums, minimax sum.

MSC: 15B33, 15A30

Поступила в редакцию: 14.03.2019

Язык публикации: английский



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