Combinatorial results for certain semigroups of order-decreasing partial isometries of a finite chain · arXivDesk1702.04485Feb 15, 201714 pages, 2 tables
Combinatorial results for certain semigroups of order-decreasing partial isometries of a finite chain
F. Al-Kharousi, R. Kehinde, A. Umar
Abstract
Let In be the symmetric inverse semigroup on Xn={1,2,…,n}
and let
and
be its subsemigroups of order-decreasing partial isometries and of order-preserving and order-decreasing partial isometries of
, respectively. In this paper we investigate the cardinalities of some equivalences on
and
which lead naturally to obtaining the order of the semigroups