Mathematical modeling of nilpotent subsemigroups of semigroups of contracting transformations of a Boolean - Selezneva, N. V. (Ukrains’kyi Matematychnyi Zhurnal, 2009)
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.