The degree of a finite set of words

TL;DR

This paper investigates properties of finitely generated submonoids of free monoids, establishing bounds on their degrees when composed with complete sets, thus generalizing known results.

Contribution

It introduces new bounds on the degree of composed submonoids, extending previous results from free submonoids to more general finitely generated cases.

Findings

If X=Y∘Z with Y complete, then d(X) ≤ d(Y)d(Z)

Generalization of properties from free submonoids to finitely generated submonoids

Provides new insights into the structure of submonoids in free monoids

Abstract

We prove several results concerning finitely generated submonoids of the free monoid. These results generalize those known for free submonoids. We prove in particular that if $X=Y\circ Z$ is a composition of finite sets of words with $Y$ complete, then $d(X)\le d(Y)d(Z)$.