%0 Journal Article
%J Fundamenta informaticae
%D 2014
%T Balances of m-bonacci words
%A Karel Břinda
%A Pelantová, Edita
%A Turek, Ondřej
%X The m-bonacci word is a generalization of the Fibonacci word to the m-letter alphabet A = {0, . . . , m − 1}. It is the unique fixed point of the Pisot–type substitution ϕm : 0 → 01, 1 → 02, . . . , (m − 2) → 0(m − 1), and (m − 1) → 0. A result of Adamczewski implies the existence of constants c (m) such that the m-bonacci word is c (m) -balanced, i.e., numbers of letter a occurring in two factors of the same length differ at most by c (m) for any letter a ∈ A. The constants c (m) have been already determined for m = 2 and m = 3. In this paper we study the bounds c (m) for a general m ≥ 2. We show that the m-bonacci word is (⌊κm⌋ + 12)-balanced, where κ ≈ 0.58. For m ≤ 12, we improve the constant c (m) by a computer numerical calculation to the value ⌈ m+1 2 ⌉.
%B Fundamenta informaticae
%V 132
%P 33-61
%8 jan
%G eng
%U http://dx.doi.org/10.3233/FI-2014-1031
%N 1
%R 10.3233/FI-2014-1011