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

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. [ABSTRACT FROM AUTHOR]