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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 7, pp. 976–985, July, 2009.
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Selezneva, N.V. Mathematical modeling of nilpotent subsemigroups of semigroups of contracting transformations of a Boolean. Ukr Math J 61, 1158–1168 (2009). https://doi.org/10.1007/s11253-009-0262-5
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DOI: https://doi.org/10.1007/s11253-009-0262-5