Résumé
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. (C) 2019 Elsevier Inc. All rights reserved.