A presentation for a submonoid of the symmetric inverse monoid

2023/10/24 by Apatsara Sareeto, Sareeto, Apatsara, Jörg Koppitz +1
Computer Science · Mathematics · #20M05 #20M18 #20M20 #Advanced Algebra and Logic #F.4 #FOS: Mathematics #Geometric and Algebraic Topology #Rings and Algebras (math.RA) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2310.15809

openalex publication_date 2023/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A fully invarient congruence relations on the free algebra on a given type induces a variety of the given type. In contrast, a congruence relation of the free algebra provides algebra of that type. This algebra is given by a so-called presentation. In the present paper, we deal with an important class of algebras of type (2), namely with semigroups of transformations on a finite set. Here, we are particularly interested in a presentation of a submonoid of the symmetric inverse monoid I_n. Our main result is a presentations for IOF_n^par, the monoid of all order-preserving, fence-preserving, and parity-preserving transformations on an n-element set.

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