Some combinatorial problems in the theory of partial transformation semigroups

A. Umar

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Let Xn = {1, 2,..., n}. On a partial transformation α : Domα ⊆ Xn → Im α ⊆ Xn of Xn the following parameters are defined: the breadth or width of α is | Domα |, the collapse of α is c(α) =| ∪t∈Imα{tα−1 :| tα−1 |≥ 2} |, fix of α is f(α) =| {x ∈ Xn : xα = x} |, the height of α is | Im α |, and the right [left] waist of α is max(Im α) [min(Im α)]. The cardinalities of some equivalences defined by equalities of these parameters on Tn, the semigroup of full transformations of Xn, and Pn the semigroup of partial transformations of Xn and some of their notable subsemigroups that have been computed are gathered together and the open problems highlighted.

Original languageEnglish
Pages (from-to)110-134
Number of pages25
JournalAlgebra and Discrete Mathematics
Volume17
Issue number1
Publication statusPublished - 2014

Keywords

  • Breadth
  • Collapse
  • Fix
  • Full transformation
  • Height and right (left) waist of a transformation
  • Idempotents and nilpotents
  • Partial transformation

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Discrete Mathematics and Combinatorics

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