General combinatorial schemas : 159 Gaussian limit distributions and exponential tails *

1 Flajolet, P. and M. Soria, General combinatorial schemas: Gaussian limit distributions and exponential tails, Discrete Mathematics 114 (1993) 159-180. Under general conditions, the number of components in combinatorial structures defined as sequences, cycles or sets of components admits a Gaussian limit distribution together with an exponential tail. The results are valid, assuming simple analytic conditions on the generating functions of the components. The proofs rely on the continuity theorem for characteristic functions and Laplace transforms as well as techniques of singularity analysis applied to algebraic and logarithmic singularities. Combinatorial applications are in the fields of graphs, permutations, random mappings, ordered partitions and polynomial factorizations.