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

Vítor H. Fernandes; Jörg Koppitz; Tiwadee Musunthia

doi:10.1007/s40840-017-0598-1

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 journal › Article › peer-review

16 Citations (Scopus)

125 Downloads (Pure)

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.

Original language	English
Pages (from-to)	2191-2211
Number of pages	21
Journal	Bulletin Of The Malaysian Mathematical Sciences Society
Volume	42
Issue number	5
DOIs	https://doi.org/10.1007/s40840-017-0598-1
Publication status	Published - 15 Sept 2019

Keywords

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

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KW - Idempotents

KW - Order-preserving

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KW - Transformation semigroups

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

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Keywords

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