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arXiv · 2205.00438

On the combinatorial and rank properties of certain subsemigroups of full contractions of a finite chain

Muhammad Mansur Zubairu·Abdullahi Umar·Muhammad Jada Aliyu
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Abstract

Let $[n]=\{1,2,\ldots,n\}$ be a finite chain and let $\mathcal{CT}_{n}$ be the semigroup of full contractions on $[n]$. Denote $\mathcal{ORCT}_{n}$ and $\mathcal{OCT}_{n}$ to be the subsemigroup of order preserving or reversing and the subsemigroup of order preserving full contractions, respectively. It was shown in [17] that the collection of all regular elements (denoted by, Reg$(\mathcal{ORCT}_{n})$ and Reg$(\mathcal{OCT}_{n}$), respectively) and the collection of all idempotent elements (denoted by E$(\mathcal{ORCT}_{n})$ and E$(\mathcal{OCT}_{n}$), respectively) of the subsemigroups $\mathcal{ORCT}_{n}$ and $\mathcal{OCT}_{n}$, respectively are subsemigroups. In this paper, we study some combinatorial and rank properties of these subsemigroups.

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Muhammad Mansur Zubairu, Abdullahi Umar, Muhammad Jada Aliyu. 2022-05-01. On the combinatorial and rank properties of certain subsemigroups of full contractions of a finite chain. https://arxiv.org/abs/2205.00438

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