论文标题
在某些订单的半群上，有限链的全收缩映射
On certain Semigroup of Order-decreasing Full Contraction Mappings of a Finite Chain
论文作者
论文摘要
令$ \ MATHCAL {CT} _n $为$ [n] = \ {1,2，\ ldots，n \} $的全部收缩映射的半群，然后让$ \ Mathcal {occt} _n $和$ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ odct} _n $是子订单和组成的子库，该子属于子序列。分别订购和保留订单的全收缩映射。在本文中，我们表明Semigroup $ \ Mathcal {odct} _n $是足够的。我们进一步研究排名属性，还获得了半群的等级，即$ \ MATHCAL {ODCT} _n $。此外，我们分别为Semigroup $ \ Mathcal {oct} _n $及其subsemigroup $ \ Mathcal {odct} _n $的自然部分订单表征。
Let $\mathcal{CT}_n$ be the semigroup of full contraction mappings on $[n]=\{1,2,\ldots,n\}$, and let $\mathcal{OCT}_n$ and $\mathcal{ODCT}_n$ be the subsemigroups consisting of all order-preserving full contraction and subsemigroup of order-decreasing and order-preserving full contraction mappings, respectively. In this paper, we show that the semigroup $\mathcal{ODCT}_n$ is left adequate. We further study the rank properties and as well obtain the rank of the semigroup, $\mathcal{ODCT}_n$. Moreover, we obtain a characterization of natural partial order for the semigroup $\mathcal{OCT}_n$ and its subsemigroup $\mathcal{ODCT}_n$, respectively.
