Analytic combinatorics : functional equations, rational and algebraic functions

Philippe Flajolet (1) , Robert Sedgewick

1 ALGO - Algorithms

This report is part of a series whose aim is to present in a synthetic way the major methods and models in analytic combinatorics. Here, we detail the case of rational and algebraic functions and discuss systematically closure properties, the location of singularities, and consequences regarding combinatorial enumeration. The theory is applied to regular and context-free languages, finite state models, paths in graphs, locally constrained permutati- ons, lattice paths and walks, trees, and planar maps.

Mots clés: ANALYTIC COMBINATORICS; FUNCTIONAL EQUATION; COMBINATORIAL ENUMERATION; GENERATING FUNCTION; ASYMPTOTIC METHODS

Domaines: Autre [cs.OH]

Philippe Flajolet, Robert Sedgewick. Analytic combinatorics : functional equations, rational and algebraic functions. [Research Report] RR-4103, INRIA. 2001. ⟨inria-00072528⟩