Turkish Journal of Mathematics
DOI
10.3906/mat-2007-69
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 $F_{\mathbb{N}}.$
Keywords
Fence, zig-zag order, order-preserving, generating set, transformation
First Page
2132
Last Page
2146
Recommended Citation
LOHAPAN, LADDAWAN; KOPPITZ, JÖRG; and WORAWISET, SOMNUEK
(2020)
"Generating sets of an infinite semigroup of transformations preserving a zig-zag order,"
Turkish Journal of Mathematics: Vol. 44:
No.
6, Article 12.
https://doi.org/10.3906/mat-2007-69
Available at:
https://journals.tubitak.gov.tr/math/vol44/iss6/12
