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

• Дата: 2009
• Автори: Selezneva, N. V., Селезньова, Н. В.
• Формат: Стаття
• Мова: Українська; Англійська
• Опубліковано: Institute of Mathematics, NAS of Ukraine 2009
• Онлайн доступ: https://umj.imath.kiev.ua/index.php/umj/article/view/3072
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

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.