On the Maximum Coefficients of Rational Formal Series in Commuting Variables

  • Christian Choffrut
  • Massimiliano Goldwurm
  • Violetta Lonati
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3340)


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.


Maximum Function Rational Series Formal Series Pattern Statistic Local Limit 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Christian Choffrut
    • 1
  • Massimiliano Goldwurm
    • 2
  • Violetta Lonati
    • 2
  1. 1.L.I.A.F.A.Université Paris VIIParisFrance
  2. 2.Dipartimento di Scienze dell’InformazioneUniversit degli Studi di MilanoMilanoItaly

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