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arXiv · 2007.10230

Generating Sets of an Infinite Semigroup of Transformations Preserving a Zig-zag Order

Laddawan Lohapan·Jörg Koppitz·Somnuek Worawiset
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Abstract

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 $F_{\mathbb{N}}$.

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Laddawan Lohapan, Jörg Koppitz, Somnuek Worawiset. 2020-07-20. Generating Sets of an Infinite Semigroup of Transformations Preserving a Zig-zag Order. https://arxiv.org/abs/2007.10230

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