On the rank of monoids of endomorphisms of a finite directed path

被引：2

作者：

Fernandes, Vitor H. ^{[1
]}

Paulista, Tania ^{[2
]}

机构：

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

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

来源：

ASIAN-EUROPEAN JOURNAL OF MATHEMATICS | 2023年 / 16卷 / 04期

关键词：

Graph endomorphisms; paths; generators; rank; SPLIT GRAPHS; TRANSFORMATIONS; SEMIGROUPS; FORM;

D O I：

10.1142/S1793557123500699

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider endomorphisms of a finite directed path from monoid generators perspective. Our main aim is to determine the rank of the monoid wEnd (P) over right arrow (n) of all weak endomorphisms of a directed path with n vertices, which is a submonoid of the widely studied monoid O-n of all order-preserving transformations of an n-chain. Also, we describe the regular elements of wEnd (P) over right arrow (n) and calculate its size and number of idempotents.

引用

页数：13

共 26 条

[1] The rank of the semigroup of transformations stabilising a partition of a finite set [J].

Araujo, Joao ;

Bentz, Wolfram ;

Mitchell, James D. ;

Schneider, Csaba .

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 2015, 159 (02) :339-353

[2] Locally strong endomorphisms of paths [J].

Arworn, Sr. ;

Knauer, U. ;

Leeratanavalee, S. .

DISCRETE MATHEMATICS, 2008, 308 (12) :2525-2532

[3] An algorithm for the numbers of endomorphisms on paths (DM13208) [J].

Arworn, Sr. .

DISCRETE MATHEMATICS, 2009, 309 (01) :94-103

[4] Ranks of Monoids of Endomorphisms of a Finite Undirected Path [J].

Dimitrova, I ;

Fernandes, V. H. ;

Koppitz, J. ;

Quinteiro, T. M. .

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2020, 43 (02) :1623-1645

[5]

Fan S., 1993, COMBINATORICS GRAPH, P117

[6]

Fan S., 1997, Acta Math. Sin, V40, P419

[7]

FERNANDES VH, 2002, SEMIGROUPS ALGORITHM, P363, DOI DOI 10.1142/9789812776884_0015

[8] The Rank of the Semigroup of All Order-Preserving Transformations on a Finite Fence [J].

Fernandes, Vitor H. ;

Koppitz, Joerg ;

Musunthia, Tiwadee .

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2019, 42 (05) :2191-2211

[9] On semigroups of endomorphisms of a chain with restricted range [J].

Fernandes, Vitor H. ;

Honyam, Preeyanuch ;

Quinteiro, Teresa M. ;

Singha, Boorapa .

SEMIGROUP FORUM, 2014, 89 (01) :77-104

[10] On the Ranks of Semigroups of Transformations on a Finite Set with Restricted Range [J].

Fernandes, Vitor H. ;

Sanwong, Jintana .

ALGEBRA COLLOQUIUM, 2014, 21 (03) :497-510

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