RUS  ENG
Full version
JOURNALS // Algebra and Discrete Mathematics // Archive

Algebra Discrete Math., 2020 Volume 30, Issue 2, Pages 161–171 (Mi adm772)

This article is cited in 1 paper

RESEARCH ARTICLE

Normal form in Hecke-Kiselman monoids associated with simple oriented graphs

R. Aragonaa, A. D'Andreab

a DISIM, University of L'Aquila, Via Vetoio, Coppito - 67100 L'Aquila, Italy
b Department of Mathematics ``Sapienza'' University of Rome, P.le Aldo Moro, 5-00185 Rome, Italy

Abstract: We generalize Kudryavtseva and Mazorchuk's concept of a canonical form of elements [9] in Kiselman's semigroups to the setting of a Hecke-Kiselman monoid $\mathbf{HK}_\Gamma$ associated with a simple oriented graph $\Gamma$. We use confluence properties from [7] to associate with each element in $\mathbf{HK}_\Gamma$ a normal form; normal forms are not unique, and we show that they can be obtained from each other by a sequence of elementary commutations. We finally describe a general procedure to recover a (unique) lexicographically minimal normal form.

Keywords: simple oriented graph, Hecke-Kiselman monoid, normal form.

MSC: 20M05, 20M10

Received: 26.03.2020
Revised: 07.12.2020

Language: English

DOI: 10.12958/adm1571



Bibliographic databases:


© Steklov Math. Inst. of RAS, 2024