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On the Number of Idempotent Partial Contraction Mappings of a Finite Chain
Oyo State College of Agriculture and Technology, Igboora, Oyo State, Nigeria
Department of Mathematics, Sultan Qaboos University, Al-Khod, Muscat, Oman
Department of Mathematics, Khalifa University of Science and Technology, Sas Al-Nakhl, Abu Dhabi, U. A. E.
- 1 Oyo State College of Agriculture and Technology, Igboora, Oyo State, Nigeria
- 2 Department of Mathematics, Sultan Qaboos University, Al-Khod, Muscat, Oman
- 3 Department of Mathematics, Khalifa University of Science and Technology, Sas Al-Nakhl, Abu Dhabi, U. A. E.
Open Journal of Discrete Mathematics·Volume 11 (2021)·Pages 94–101·Published 8 June 2021·DOI10.4236/ojdm.2021.113007
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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 .
KeywordsHeightRight (Left) Waist and Fix of a TransformationIdempotents
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