The Rank of the Semigroup of All Order-Preserving Transformations on a Finite Fence

Vítor H. Fernandes, Jörg Koppitz, Tiwadee Musunthia

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

A zig-zag (or fence) order is a special partial order on a (finite) set. In this paper, we consider the semigroup TFn of all order-preserving transformations on an n-element zig-zag-ordered set. We determine the rank of TFn and provide a minimal generating set for TFn. Moreover, a formula for the number of idempotents in TFn is given.

Original languageEnglish
Pages (from-to)2191-2211
Number of pages21
JournalBulletin Of The Malaysian Mathematical Sciences Society
Volume42
Issue number5
DOIs
Publication statusPublished - 15 Sep 2019

Keywords

  • Fence
  • Idempotents
  • Order-preserving
  • Rank of semigroup
  • Transformation semigroups
  • Zig-zag order

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