论文标题
在有限链的全部收缩的某些子群中的组合和等级属性上
On the combinatorial and rank properties of certain subsemigroups of full contractions of a finite chain
论文作者
论文摘要
令$ [n] = \ {1,2，\ ldots，n \} $为有限的链，让$ \ Mathcal {ct} _ {n} $是$ [n] $的全部收缩的半群。表示$ \ MATHCAL {ORCT} _ {n} $和$ \ MATHCAL {OCT} _ {n} $作为保留或反转的订单的子群，并分别保留完整收缩的订单中的子群。在[17]中表明，所有常规元素的集合（由Reg $（\ Mathcal {orct} _ {n}）$和reg $（分别分别为\ Mathcal {oct} _ {n} $），以及所有didempotent elements的收集E $（\ Mathcal {oct} _ {n} $）分别为$ \ Mathcal {orct} _ {n} $和$ \ MATHCAL {oct} _ {n} $，分别为supmigroups。在本文中，我们研究了这些子群的一些组合和等级。
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.
