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Templates for the k-binomial complexity of the Tribonacci word
Authors
Marie Lejeune
Michel Rigo
Matthieu Rosenfeld
Publication date
1 January 2020
Publisher
'Elsevier BV'
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Abstract
Consider 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≥2, 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. © 2019 Elsevier Inc
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Last time updated on 16/03/2020