Systems of numeration and fractal functions relating to substitutions (French)
Theoretical Computer Science - Conference on arithmetics and coding systems, Marseille-Luminy, June 1987
Sequences defined by iterated morphisms
Sequences
A characterization of substitutive sequences using return words
Discrete Mathematics
Theoretical Computer Science
Balanced sequences and optimal routing
Journal of the ACM (JACM)
Fraenkel's conjecture for six sequences
Discrete Mathematics
Balance properties of multi-dimensional words
Theoretical Computer Science
Generalized balances in Sturmian words
Discrete Applied Mathematics
Complexité des Facteurs des Mots Infinis Engendrés par Morphimes Itérés
Proceedings of the 11th Colloquium on Automata, Languages and Programming
Abelian complexity and abelian co-decomposition
Theoretical Computer Science
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An infinite word defined over a finite alphabet A is balanced if for any pair (ω,ω') of factors of the same length and for any letter a in the alphabet ||ω|a - |ω'|a| ≤ 1, where |ω|a denotes the number of occurrences of the letter a in the word ω. In this paper, we generalize this notion and introduce a measure of balance for an infinite sequence. In the case of fixed points of primitive substitutions, we show that the asymptotic behaviour of this measure is in part ruled by the spectrum of the incidence matrix associated with the substitution. Connections with frequencies of letters and other balance properties are also discussed.