combinatorics on words; binomial coefficients; k-binomial complexity; Tribonacci word
Abstract :
[en] Consider the k-binomial equivalence: two finite words are equivalent if they share the same subwords of length at most k with the same multiplicities. With this relation, the k-binomial complexity of an infinite word x maps the integer n to the number of pairwise non-equivalent factors of length n occurring in x. In this paper based on the notion of template introduced by Currie et al., we show that, for all k > 1, the k-binomial complexity of the Tribonacci word coincides with its usual factor complexity p(n)=2n+1. A similar result was already known for Sturmian words but the proof relies on completely different techniques that seemingly could not be applied for Tribonacci.
Disciplines :
Mathematics Computer science
Author, co-author :
Lejeune, Marie ; Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes
Rigo, Michel ; Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes
Rosenfeld, Matthieu ; Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes
Language :
English
Title :
Templates for the k-binomial complexity of the Tribonacci word
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