On Periodicity of Generalized Pseudostandard Words

Generalized pseudostandard words were introduced by de Luca and De Luca in 2006. In comparison to the palindromic and pseudopalindromic closure, only little is known about the generalized pseudopalindromic closure and the associated generalized pseudostandard words. In this paper we provide a necess...

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Bibliographic Details
Published inThe Electronic journal of combinatorics Vol. 23; no. 1
Main Authors Florian, Josef, Dvořáková, L'ubomíra
Format Journal Article
LanguageEnglish
Published 11.01.2016
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Summary:Generalized pseudostandard words were introduced by de Luca and De Luca in 2006. In comparison to the palindromic and pseudopalindromic closure, only little is known about the generalized pseudopalindromic closure and the associated generalized pseudostandard words. In this paper we provide a necessary and sufficient condition for their periodicity over a binary and a ternary alphabet. More precisely, we describe how the directive bi-sequence of a generalized pseudostandard word has to look like in order to correspond to a periodic word. We state moreover a conjecture concerning a necessary and sufficient condition for periodicity over any alphabet.
ISSN:1077-8926
1077-8926
DOI:10.37236/4771