TITLE:
On the Number of Idempotent Partial Contraction Mappings of a Finite Chain
AUTHORS:
Oladapo Adekunle Ojo, Fatma Salim Ali Al-Kharousi, Abdullahi Umar
KEYWORDS:
Height, Right (Left) Waist and Fix of a Transformation, Idempotents
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.11 No.3,
July
13,
2021
ABSTRACT: Let be the partial symmetric semigroup on and let and be its subsemigroups of order-preserving contractions and order-preserving, order-decreasing contractions mappings of , respectively. In this paper we investigate the cardinalities of and , the set idempotents of and , respectively. We also investigate the cardinalities of certain equivalences on and .