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.