%0 Journal Article
%T On the Number of Idempotent Partial Contraction Mappings of a Finite Chain
%A Oladapo Adekunle Ojo
%A Fatma Salim Ali Al-Kharousi
%A Abdullahi Umar
%J Open Journal of Discrete Mathematics
%P 94-101
%@ 2161-7643
%D 2021
%I Scientific Research Publishing
%R 10.4236/ojdm.2021.113007
%X <span style=\"font-family:Verdana;\">Let <img alt=\"\" src=\"Edit_1798cf4c-b9a5-4ada-b2d4-9fbf535a6d28.png\" />be the partial symmetric semigroup on <img alt=\"\" src=\"Edit_86c31e58-0588-44fc-8ff3-78c73dc14be6.png\" />and let <img alt=\"\" src=\"Edit_09f7ec2a-49d1-463d-952e-93fbe00740cd.png\" />and <img alt=\"\" src=\"Edit_4aca07c1-9a36-44b6-83af-46fdd6278ca4.png\" />be its subsemigroups of order-preserving contractions and order-preserving, order-decreasing contractions mappings of <img alt=\"\" src=\"Edit_72d2bbdf-2b96-4812-a993-f49640bb98c9.png\" />, respectively. In this paper we investigate the cardinalities of <img alt=\"\" src=\"Edit_95038cdc-5496-495f-bfb9-29c817ba2df4.png\" />and <img alt=\"\" src=\"Edit_f8d3d782-ff8c-43b3-84af-d21a3f4291d5.png\" />, the set idempotents of <img alt=\"\" src=\"Edit_ac8237f8-83ec-4767-9029-b546377bf106.png\" />and <img alt=\"\" src=\"Edit_8b1bf8bf-7472-453c-965d-7308da5b4f4c.png\" />, respectively. We also investigate the cardinalities of certain equivalences on <img alt=\"\" src=\"Edit_e5f7aec4-67c1-48ba-8d03-ea6ceb2e7627.png\" />and <img alt=\"\" src=\"Edit_42a31943-fe9d-4ea8-8999-3aadb705fb38.png\" />.</span>
%K Height
%K Right (Left) Waist and Fix of a Transformation
%K Idempotents
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=110485