论文标题
在有限套件上的循环逆上的单体上
On the cyclic inverse monoid on a finite set
论文作者
论文摘要
在本文中，我们研究了带有$ n $元素的$ω_n$上的循环互动的monoid $ \ ci_n $，即$ n $ ements的对称的submonoid在$ω_n$上是由$ω_n$组成的对称逆元模式，这些元素由$ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ ncly上的元素的所有限制组成。我们表明，$ \ ci_n $的排名$ 2 $（对于$ n \ geqslant2 $）和$ n2^n-n+1 $元素。此外，我们在$ n+1 $发电机和$ \ frac {1} {2}（n^2+3n+4）$上提供$ \ ci_n $的演示文稿，以及$ 2 $生成器和$ \ frac {1} {1} {2} {2} {2}（n^2-n+6）$ camenate。我们还考虑了$ \ ci_n $的显着逆下monoid $ \ oci_n $，其所有订单保留转换构成。我们证明$ \ oci_n $具有排名$ n $和$ 3 \ cdot 2^n-2n-1 $元素。此外，我们在$ n+2 $发电机上展示了$ \ oci_n $的演示文稿，$ \ frac {1} {2} {2}（n^2+3n+8）$关系和$ n $发电机和$ \ \ \ \ frac {1} {1} {2} {2} {2}（n^2+3n）$关系。
In this paper we study the cyclic inverse monoid $\CI_n$ on a set $Ω_n$ with $n$ elements, i.e. the inverse submonoid of the symmetric inverse monoid on $Ω_n$ consisting of all restrictions of the elements of a cyclic subgroup of order $n$ acting cyclically on $Ω_n$. We show that $\CI_n$ has rank $2$ (for $n\geqslant2$) and $n2^n-n+1$ elements. Moreover, we give presentations of $\CI_n$ on $n+1$ generators and $\frac{1}{2}(n^2+3n+4)$ relations and on $2$ generators and $\frac{1}{2}(n^2-n+6)$ relations. We also consider the remarkable inverse submonoid $\OCI_n$ of $\CI_n$ constituted by all its order-preserving transformations. We show that $\OCI_n$ has rank $n$ and $3\cdot 2^n-2n-1$ elements. Furthermore, we exhibit presentations of $\OCI_n$ on $n+2$ generators and $\frac{1}{2}(n^2+3n+8)$ relations and on $n$ generators and $\frac{1}{2}(n^2+3n)$ relations.
