<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Fernandes, Vítor H.</style></author><author><style face="normal" font="default" size="100%">Koppitz, J.</style></author><author><style face="normal" font="default" size="100%">Musunthia, T.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">The rank of the semigroup of all order-preserving transformations on a finite fence</style></title><secondary-title><style face="normal" font="default" size="100%">Bulletin of the Malaysian Mathematical Sciences Society (DOI: 10.1007/s40840-017-0598-1)</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2019</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://rdcu.be/FYNs</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">42</style></volume><pages><style face="normal" font="default" size="100%">2191-2211</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;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&lt;br /&gt;
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.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">5</style></issue></record></records></xml>