The degree of a finite set of words

preprint2022arXivOpen access

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 $d(X)\le d(Y)d(Z)$ .

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The degree of a finite set of words

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