$L$-Primitive Words in Submonoids

Abstract: This work considers a natural generalization of primitivity with respect to a language. Given a language $L$, a nonempty word $w$ is said to be $L$-primitive if $w$ is not a proper power of any word in $L$. After ascertaining the number of primitive words in submonoids of a free monoid, the work proceeds to count $L$-primitive words in submonoids of a free monoid. The work also studies the distribution of $L$-primitive words in certain subsets of free monoids.