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

被引：16

作者：

Fernandes, Vitor H. ^{[1
]}

Koppitz, Joerg ^{[2
,3
]}

Musunthia, Tiwadee ^{[4
]}

机构：

[1] Univ Nova Lisboa, Fac Ciencias & Tecnol, Dept Matemat, CMA, P-2829516 Monte De Caparica, Caparica, Portugal

[2] Univ Potsdam, Inst Math, D-14476 Potsdam, Germany

[3] Bulgarian Acad Sci, Inst Math & Informat, Acad G Bonchev Str Bl 8, BU-1113 Sofia, Bulgaria

[4] Silpakorn Univ, Fac Sci, Dept Math, Nakhon Pathom 73000, Thailand

来源：

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY | 2019年 / 42卷 / 05期

关键词：

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

D O I：

10.1007/s40840-017-0598-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：2191 / 2211

页数：21

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