2018
Том 70
№ 5

Mathematical modeling of nilpotent subsemigroups of semigroups of contracting transformations of a Boolean

Selezneva N. V.

Abstract

We study mathematical models of the structure of nilpotent subsemigroups of the semigroup $PTD(B_n)$ of partial contracting transformations of a Boolean, the semigroup $TD(B_n)$ of full contracting transformations of a Boolean, and the inverse semigroup $ISD(B_n)$ of contracting transformations of a Boolean. We propose a convenient graphical representation of the semigroups considered. For each of these semigroups, the uniqueness of its maximal nilpotent subsemigroup is proved. For $PTD(B_n)$ and $TD(B_n)$, the capacity of a maximal nilpotent subsemigroup is calculated. For $ISD(B_n)$, we construct estimates for the capacity of a maximal nilpotent subsemigroup and calculate this capacity for small $n$. For all indicated semigroups, we describe the structure of nilelements and maximal nilpotent subsemigroups of nilpotency degree $k$ and determine the number of elements and subsemigroups for some special cases.

English version (Springer): Ukrainian Mathematical Journal 61 (2009), no. 7, pp 1158-1168.

Citation Example: Selezneva N. V. Mathematical modeling of nilpotent subsemigroups of semigroups of contracting transformations of a Boolean // Ukr. Mat. Zh. - 2009. - 61, № 7. - pp. 976-985.

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