Adamczewski Boris
Balances for fixed points of primitive substitutions.
An infinite word defined over a finite alphabet ${\cal A}$ is balanced if
for any pair $(\omega,\omega')$ of factors of the same length and for any
letter $a$ in the alphabet
$$\left\vert\vert\omega\vert_a\vert\omega'\vert_a
\right\vert\leq 1,$$
where $\vert\omega\vert_a$ denotes the number of occurrences of the letter $a$
in the word $\omega$. 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. Connexions with frequency and other balance
properties are also discussed.
