An alphabet reduction is a 1-uniform morphism that maps a word to an image that contains a smaller number of different letters. In the present paper we investigate the effect of alphabet reductions on morphically primitive words, i. e., words that are not a fixed point of a nontrivial morphism. Our first main result answers a question on the existence of unambiguous alphabet reductions for such...

We present here the notion of signature of trees and of languages, and its relationships with the theory of numeration systems. The signature of an ordered infinite tree (of bounded degree) is an infinite (bounded) sequence of integers, the sequence of the degrees of the nodes taken in the visit order of the canonical breadth-first traversal of the tree. A prefix-closed language defines such a ...

In the present paper, we obtain some interesting properties for mero-morphic analytic functions related to Cho-Kwon-Srivastava Operator defined by means of an operator recently given by Ghanim and Darus.

Episturmian morphisms constitute a powerful tool to study episturmian words. Indeed, any episturmian word can be infinitely decomposed over the set of pure episturmian morphisms. Thus, an episturmian word can be defined by one of its morphic decompositions or, equivalently, by a certain directive word. Here we characterize pairs of words directing a common episturmian word. We also propose a wa...

In this paper we solve some open problems related to (pseudo)palindrome closure operators and to the infinite words generated by their iteration, that is, standard episturmian and pseudostandard words. We show that if θ is an involutory antimorphism of A, then both θ-palindromic closures of any factor of a θ-standard word are also factors of some θ-standard word. We also introduce the class of ...