We survey known results and open problems in abelian combinatorics on words. Abelian
combinatorics on words is the extension to the commutative setting of the classical theory of …

In this paper we introduce and study a family of complexity functions of infinite words
indexed by k∈ Z+∪{+∞}. Let k∈ Z+∪{+∞} and A be a finite non-empty set. Two finite …

The notion of Abelian complexity of infinite words was recently used by the three last authors
to investigate various Abelian properties of words. In particular, using van der Waerden's …

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The properties characterizing Sturmian words are considered for words on multiliteral
alphabets. We summarize various generalizations of Sturmian words to multiliteral …

Abelian Complexity of Thue-Morse Word over a Ternary Alphabet | SpringerLink Skip to main
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According to a result of Richomme, Saari and Zamboni, the abelian complexity of the
Tribonacci word satisfies $\rho^{\mathrm {ab}}(n)\in\{3, 4, 5, 6, 7\} $ for each $ n\in\mathbb …

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 …

The subword complexity of an infinite word counts the number of subwords of a given length,
while the abelian complexity counts this number up to letter permutation. Although a lot of …

We propose a technique for exploring the abelian complexity of recurrent infinite words,
focusing particularly on infinite words associated with Parry numbers. Using that technique …