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

Year 2021, Volume: 9 Issue: 4, 170 - 175, 31.12.2021

Kemal Toker

https://doi.org/10.36753/mathenot.807993

Cited By: 1

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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