The Monoid Rank and Monoid Presentation of Order-Preserving and Order-Decreasing Full Contraction Mappings

Authors : Kemal TOKER

Pages : 170-175

Doi:10.36753/mathenot.807993

View : 32 | Download : 11

Publication Date : 2021-12-31

Article Type : Research Paper

Abstract :Let $n \in \mathbb{Z}^{+}$ and $X_{n}=\{1,2,\ldots,n\}$ be a finite set. Let $\mathcal ODCT_{n}$ be the order-preserving and order-decreasing full contraction mappings on $X_{n}$. It is well known that $\mathcal ODCT_{n}$ is a monoid. In this paper, we have found the monoid rank and monoid presentation of $\mathcal ODCT_{n}$. In particular, we have proved that monoid rank of $\mathcal ODCT_{n}$ is $n-1$ for $n \in \mathbb{Z}^{+}$ and $$ is a monoid presentation of $\mathcal ODCT_{n}$ for $n \geq 3$.
Keywords : Contraction mappings, Generating set, Monoid Presentation

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