Homogeneous finitely presented monoids of linear growth

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 $a<w>b$, where $a,b,w$ are elements of $M$ and $<w>$ 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 $a{w}^{n}b$ 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.

5 pp

Cited by in corpus (1)

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