The Monoid Rank and Monoid Presentation of Order-Preserving and Order-Decreasing Full Contraction Mappings
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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- ISSN: 2147-6268
- Yayın Aralığı: Yılda 4 Sayı
- Başlangıç: 2013
- Yayıncı: -