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
收藏
页码：2191 / 2211
页数：21
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