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

  • N. V. Selezneva
Article
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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.

Keywords

Linear Order Zero Level Zero Element Finite Semigroup Green Relation 
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References

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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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