Combinatorics, Probability & Computing

Table of Contents - 2002 - Volume 11, Issue 01  


Mappings on Decomposable Combinatorial Structures: Analytic Approach

E. MANSTAVICIUS a1
a1 Department of Mathematics and Informatics, Vilnius University, Naugarduko Str. 24, LT2600 Vilnius, Lithuania (e-mail: eugenijus.manstavicius@maf.vu.lt)

Abstract

On the class of labelled combinatorial structures called assemblies we define complex-valued multiplicative functions and examine their asymptotic mean values. The problem reduces to the investigation of quotients of the Taylor coefficients of exponential generating series having Euler products. Our approach, originating in probabilistic number theory, requires information on the generating functions only in the convergence disc and rather weak smoothness on the circumference. The results could be applied to studying the asymptotic value distribution of decomposable mappings defined on assemblies.

(Received April 6 1999)
(Revised August 1 2001)