Combinatorial results for certain semigroups of order-preserving full contraction mappings of a finite chain

Abstract

Let ${\mathcal{T}}_n$ be the full symmetric semigroup on $X_n=\{1,2,...,n\}$ and let ${\mathcal{O}\mathcal{C}\mathcal{T}}_n$ and ${\mathcal{O}\mathcal{R}\mathcal{C}\mathcal{T}}_n$ be its subsemigroups of order-preserving and order-preserving or order-reversing full contraction mappings of $X_n$, respectively. In this paper we investigate the cardinalities of some equivalences on ${\mathcal{O}\mathcal{C}\mathcal{T}}_n$ and ${\mathcal{O}\mathcal{R}\mathcal{C}\mathcal{T}}_n$ which lead naturally to obtaining the orders of these subsemigroups.

11 pages. arXiv admin note: text overlap with arXiv:1101.0049 by other authors There are two authors now instead of the previous three

Cited by in corpus (3)

• On certain semigroups of partial contractions of a finite chain
• Regularity and Green's relations for the semigroup of partial contractions of a finite chain
• On certain semigroups of full contractions of a finite chain