论文标题
生成一组无限的转换的半群，以保存锯齿形订单
Generating Sets of an Infinite Semigroup of Transformations Preserving a Zig-zag Order
论文作者
论文摘要
锯齿形订单就像有向路径一样，只有交替的方向。 Fenandes等人确定了保留Zig-Zag顺序的有限集中所有完整转换的半群的生成最小尺寸。在2019年。本文介绍了所有自然编号的所有完整转换的semigroup $ f _ {\ mathbb {n}} $的集合，以保留Zig-Zag顺序。我们证明$ f _ {\ mathbb {n}} $没有最小的生成集，并呈现了两个特定的无限降低的生成链的生成集的链条$ f _ {\ mathbb {n}} $。
A zig-zag order is like a directed path, only with alternating directions. A generating set of minimal size for the semigroup of all full transformations on a finite set preserving the zig-zag order was determined by Fenandes et al. in 2019. This paper deals with generating sets of the semigroup $F_{\mathbb{N}}$ of all full transformations on the set of all natural numbers preserving the zig-zag order. We prove that $F_{\mathbb{N}}$ has no minimal generating sets and present two particular infinite decreasing chains of generating sets of $F_{\mathbb{N}}$.
