On Hasse diagrams connected with the poset (1, 2, 7)

Stoika, M. V., Styopochkina, M. V. (2020). On Hasse diagrams connected with the poset (1, 2, 7). Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics(4), 16–19. https://doi.org/10.17721/1812-5409.2020/4.2

Representations of posets introduced in 1972 by L. O. Nazarova and A. V. Roiter, arise when solving many problems in various fields of mathematics. One of the most important problem in the theory of representations of any objects is a description of the cases of representation finite type and representation tame type. The first of these problems for posets was solved by M. M. Kleiner, and the second L. O, Nazarova. M. M. Kleiner proved that a poset has finite type if and only if it does not contain subsets of the form (1, 1, 1, 1), (2, 2, 2), (1, 3, 3), (1, 2, 5) and (?, 4), which are called the critical sets. A generalization of this criterion to the tame case was obtained by L. O. Nazarova. The corresponding sets are called supercritical and they consist of the posets (1, 1, 1, 1, 1), (1, 1, 1, 2), (2, 2, 3), (1, 3, 4), (1, 2, 6) and (?, 5). V. M. Bondarenko proposed a generalization of the critical and supercritical posets, calling them 1-oversupercritical. This paper studies the combinatorial properties of one of such sets.Key words: poset, graph, critical and supercritical poset, 1-oversupercritical poset, anti-isomorphism, Hasse diagrams, minimax equivalence.Pages of the article in the issue: 16 - 19Language of the article: English