Perfect submonoids of dominant weights

Perfect connected-dominant graphs

If D is a dominating set and the induced subgraph G(D) is connected, then D is a connected dominating set. The minimum size of a connected dominating set in G is called connected domination number γc(G) of G. A graph G is called a perfect connected-dominant graph if γ(H) = γc(H) for each connected induced subgraph H of G. We prove that a graph is a perfect connected-dominant graph if and only i...

The Partial Order of Dominant Weights

Completing prefix codes in submonoids

Let M be a submonoid of the free monoid A∗, and let X ⊆ M be a variable length code (for short a code). X is weakly M-complete if any word in M is a factor of some word in X∗ [J. Néraud, C. Selmi, Free monoid theory: maximality and completeness in arbitrary submonoids, Internat. J. Algorithms Comput. 13(5) (2003) 507–516]. Given a code X ⊆ M , we are interested in the construction of a weakly M...

$L$-Primitive Words in Submonoids

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 ...

On finitely generated submonoids of free groups

We prove that the classes of graded monoids, regular monoids and Kleene monoids coincide for submonoids of free groups. We also prove that it is decidable whether or not a finitely generated submonoid of a free group is graded, and solve the homomorphism and isomorphism problems for graded submonoids of free groups. This generalizes earlier results for submonoids of free monoids. MSC: 20E05; 20...