General combinatorial schemas: gaussian limit distributions and exponential tails (1990).

Content Provider	CiteSeerX
Author	Flajolet, Philippe Soria, Michèle Fraenkel, Aviezri S.
Abstract	. 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 continuity theorem for characteristic functions, 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. Keywords : combinatorial analysis, generating functions, singularity analysis, limit distributions, exponential tails. 1 Introduction Vassilii Leonidovich Goncharov established in 1944 that the number of cycles in a random permutation of large size approaches a normal distribution, see Knuth's account in [19, p. 103]. Many results of a similar type are now known fo...
File Format	PDF
Publisher Date	1990-01-01
Access Restriction	Open
Subject Keyword	Exponential Tail Gaussian Limit Distribution General Combinatorial Schema Singularity Analysis Large Size Introduction Vassilii Leonidovich Goncharov Random Permutation Simple Analytic Condition Limit Distribution Logarithmic Singularity Combinatorial Structure General Condition Combinatorial Application Continuity Theorem Characteristic Function Random Mapping Similar Type Normal Distribution Many Result Combinatorial Analysis Polynomial Factorization
Content Type	Text