Combinatorial results for certain semigroups of order-decreasing partial isometries of a finite chain

F. Al-Kharousi; R. Kehinde; A. Umar

Combinatorial results for certain semigroups of order-decreasing partial isometries of a finite chain

Group Theory 2017-02-16 v1

Authors: F. Al-Kharousi , R. Kehinde , A. Umar

Abstract

Let ${\cal I}_n$ be the symmetric inverse semigroup on $X_n = \{1, 2, \ldots , n\}$ and let ${\cal DDP}_n$ and ${\cal ODDP}_n$ be its subsemigroups of order-decreasing partial isometries and of order-preserving and order-decreasing partial isometries of $X_n$ , respectively. In this paper we investigate the cardinalities of some equivalences on ${\cal DDP}_n$ and ${\cal ODDP}_n$ which lead naturally to obtaining the order of the semigroups

Keywords

symmetric inverse semigroup order-decreasing partial isometry subsemigroup equivalence cardinality finite chain semigroup order

Cite

@article{arxiv.1702.04485,
  title  = {Combinatorial results for certain semigroups of order-decreasing partial isometries of a finite chain},
  author = {F. Al-Kharousi and R. Kehinde and A. Umar},
  journal= {arXiv preprint arXiv:1702.04485},
  year   = {2017}
}

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14 pages, 2 tables

Combinatorial results for certain semigroups of order-decreasing partial isometries of a finite chain

Abstract

Keywords

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