论文标题
有限套装的订单，围栏和平等部分注射的半群的等级
The rank of the semigroup of order-, fence-, and parity-preserving partial injections on a finite set
论文作者
论文摘要
由于众所周知的Wagner-Preston定理，在有限集集（对称逆半群）上的所有部分注射的单体特别感兴趣。在本文中，我们向对称反向半群的亚monoi的研究进行了前进。我们探索了$ n $ element链上所有订单，围栏和平等转换的单体。我们还表征了该单体中的转换，并表明它的排名$ 3N-6 $。特别是，我们为$ a_n $生成的转换提供了最小尺寸的生成集$ a_n $。
The monoid of all partial injections on a finite set (the symmetric inverse semigroup) is of particular interest because of the well-known Wagner-Preston Theorem. In this article, we step forward the study of a submonoid of the symmetric inverse semigroup. We explore the monoid of all order-, fence-, and parity-preserving transformations on an $n$-element chain. We also characterize the transformations in that monoid and show that it has a rank $3n-6$. In particular, we provide a generating set $A_n$ of minimal size and exhibit concrete normal forms for the transformations generated by $A_n$.
