Generating sets of an infinite semigroup of transformations preserving a zig-zag order.

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 FN of all full transformations on the set of all natural numbers preserving the zig-zag order. We prove that FN has no minimal generating sets and present two particular infinite decreasing chains of generating sets of FN. [ABSTRACT FROM AUTHOR]