Abstract
We study the maximum function of any ℝ + -rational formal series S in two commuting variables, which assigns to every integer n ∈ ℕ, the maximum coefficient of the monomials of degree n. We show that if S is a power of any primitive rational formal series, then its maximum function is of the order Θ(n k / 2 λ n) for some integer k ≥ –1 and some positive real λ. Our analysis is related to the study of limit distributions in pattern statistics. In particular, we prove a general criterion for establishing Gaussian local limit laws for sequences of discrete positive random variables.
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Choffrut, C., Goldwurm, M., Lonati, V. (2004). On the Maximum Coefficients of Rational Formal Series in Commuting Variables. In: Calude, C.S., Calude, E., Dinneen, M.J. (eds) Developments in Language Theory. DLT 2004. Lecture Notes in Computer Science, vol 3340. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30550-7_10
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DOI: https://doi.org/10.1007/978-3-540-30550-7_10
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