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 …

Formal Languages, Automaton and Numeration Systems presents readers with a review of
research related to formal language theory, combinatorics on words or numeration systems …

The interplay between words, computability, algebra and arithmetic has now proved its
relevance and fruitfulness. Indeed, the cross-fertilization between formal logic and finite …

We introduce and study a complexity function on words cx (n), called cyclic complexity,
which counts the number of conjugacy classes of factors of length n of an infinite word x. We …

We study the combinatorics of vtm, a variant of the Thue-Morse word generated by the non-
uniform morphism 0↦ 012, 1↦ 02, 2↦ 1 starting with 0. This infinite ternary sequence …

We prove that a sequence satisfying a certain symmetry property is $2 $-regular in the sense
of Allouche and Shallit, ie, the $\mathbb {Z} $-module generated by its $2 $-kernel is finitely …

Abelian Complexity of Thue-Morse Word over a Ternary Alphabet | SpringerLink Skip to main
content Advertisement Springer Nature Link Account Menu Find a journal Publish with us Track …

In the first part of this survey, we present classical notions arising in combinatorics on words:
growth function of a language, complexity function of an infinite word, pattern avoidance …

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 …

An abelian antipower of order k (or simply an abelian k-antipower) is a concatenation of k
consecutive words of the same length having pairwise distinct Parikh vectors. This definition …