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 $F_{ \mathbb{ N}}$.
Categories: math.RA