@article {11289,
title = {The rank of the semigroup of all order-preserving transformations on a finite fence},
journal = {Bulletin of the Malaysian Mathematical Sciences Society (DOI: 10.1007/s40840-017-0598-1)},
volume = {42},
year = {2019},
pages = {2191-2211},
abstract = {A zig-zag (or fence) order is a special partial order on a (finite) set. In this paper, we consider the semigroup $TF_{n}$ of all

order-preserving transformations on an $n$-element zig-zag ordered set. We determine the rank of $TF_{n}$ and provide a minimal generating set for $TF_{n}$. Moreover, a formula for the number of idempotents in $TF_{n}$ is given.

},
url = {http://rdcu.be/FYNs},
author = {Fernandes, V{\'\i}tor H. and Koppitz, J. and Musunthia, T.}
}