Enumerative combinatorics
Combinatorial enumeration of groups, graphs, and chemical compounds
Combinatorial enumeration of groups, graphs, and chemical compounds
Combinatorial directional derivatives and Taylor expansions (French)
Discrete Mathematics
Discrete Mathematics - Special volume: algebraic combinatorics
Counting asymmetric enriched trees
Journal of Symbolic Computation - Special issue on symbolic computation in combinatorics
A calculus for the random generation of labelled combinatorial structures
Theoretical Computer Science
Modern computer algebra
Fast Algorithms for Manipulating Formal Power Series
Journal of the ACM (JACM)
CAAP '90 Proceedings of the 15th Colloquium on Trees in Algebra and Programming
CAAP '92 Proceedings of the 17th Colloquium on Trees in Algebra and Programming
Journal of Symbolic Computation
Boltzmann Samplers for the Random Generation of Combinatorial Structures
Combinatorics, Probability and Computing
Fast computation of power series solutions of systems of differential equations
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Analytic Combinatorics
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We consider systems of recursively defined combinatorial structures. We give algorithms checking that these systems are well founded, computing generating series and providing numerical values. Our framework is an articulation of the constructible classes of Flajolet and Sedgewick with Joyal@?s species theory. We extend the implicit species theorem to structures of size zero. A quadratic iterative Newton method is shown to solve well-founded systems combinatorially. From there, truncations of the corresponding generating series are obtained in quasi-optimal complexity. This iteration transfers to a numerical scheme that converges unconditionally to the values of the generating series inside their disk of convergence. These results provide important subroutines in random generation. Finally, the approach is extended to combinatorial differential systems.