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

  • N. V. Selezneva

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.


Linear Order Zero Level Zero Element Finite Semigroup Green Relation 
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  1. 1.
    A. Clifford and G. Preston, The Algebraic Theory of Semigroups, American Mathematical Society, Providence, RI (1967).zbMATHGoogle Scholar
  2. 2.
    N. V. Selezneva, “Relationship between the nilpotency in B N and acyclic graphs,” in: Proceedings of the 12 th International Scientific Conference devoted to Academician M. Kravchuk (May 15–17, 2008, Kiev) [in Ukrainian], Kiev (2008), Part. 1, p. 783.Google Scholar
  3. 3.
    O. Ganyushkin and V. Mazorchuk, On Classification of Maximal Nilpotent Subsemigroups, Preprint No. 37, Uppsala University, Uppsala (2005).Google Scholar
  4. 4.
    G. Lallement, Semigroups and Combinatorial Applications, Wiley, New York (1979).zbMATHGoogle Scholar
  5. 5.
    O. Ganyushkin and V. Mazorchuk, “Combinatorics of nilpotents in IS n ,” Ann. Combinat., 8, 161–175 (2004).MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  • N. V. Selezneva
    • 1
  1. 1.Shevchenko Kyiv National UniversityKyivUkraine

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