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Communication Dans Un Congrès Année : 2004

On the maximum coefficients of the rational formal series in commuting variables

Résumé

We study the maximum function of any R+ -rational formal series S in two commuting variables, which assigns to every integer n ∈ R, 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(nk/2 λn ) 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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Dates et versions

hal-00158288 , version 1 (28-06-2007)

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  • HAL Id : hal-00158288 , version 1

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Christian Choffrut, Violetta Lonati, Massimiliano Goldwurm. On the maximum coefficients of the rational formal series in commuting variables. Developments in Language Theory, Dec 2004, auckland, New Zealand. pp.114-126. ⟨hal-00158288⟩
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