Homogeneous finitely presented monoids of linear growth

2017/12/16 by Dmitri Piontkovski, Piontkovski, Dmitri · 1 citation
Computer Science · Mathematics · #20M05 #Advanced Topology and Set Theory #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Rings and Algebras (math.RA) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1712.06022

openalex publication_date 2017/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

If a finitely generated monoid M is defined by a finite number of degree-preserving relations, then it has linear growth if and only if it can be decomposed into a finite disjoint union of subsets (which we call "sandwiches") of the form ab, where a,b,w are elements of M and denotes the monogenic semigroup generated by w. Moreover, the decomposition can be chosen in such a way that the sandwiches are either singletons or "free" ones (meaning that all elements a wⁿ b in each sandwich are pairwise different). So, the minimal number of free sandwiches in such a decomposition is a numerical invariant of a homogeneous (and conjecturally, non-homogeneous) finitely presented monoid of linear growth.

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