On the maximum coefficients of rational formal series in commuting variables

Authors:
Christian Choffrut;Massimiliano Goldwurm;Violetta Lonati
Affiliations:
L.I.A.F.A., Université Paris VII, Paris, France;Dipartimento di Scienze dell’Informazione, Universit degli Studi di Milano, Milano, Italy;Dipartimento di Scienze dell’Informazione, Universit degli Studi di Milano, Milano, Italy
Venue:
DLT'04 Proceedings of the 8th international conference on Developments in Language Theory
Year:
2004

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Preface

Theoretical Computer Science - In honour of Professor Christian Choffrut on the occasion of his 60th birthday

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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(nk / 2λn) 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.