Volume no :19, Issue no: 1, March (2018)

Journal of Algebra, Number Theory: Advances and Applications

COMBINATORIAL RESULTS FOR CERTAIN SEMIGROUPS OF ORDER-DECREASING PARTIAL ISOMETRIES OF A FINITE CHAIN

Author's: F. Al-Kharousi, R. Kehinde and A. Umar
Pages: [29] - [49]
Received Date: December 1, 2017
Submitted by:
DOI: http://dx.doi.org/10.18642/jantaa_7100121902

Abstract

Let be the symmetric inverse semigroup on 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.

Keywords

partial one-one transformation, partial isometries, height, right (left) waist, right (left) shoulder and fix of a transformation, idempotents and nilpotents.