Guessing a Conjecture in Enumerative Combinatorics and Proving It with a Computer Algebra System - Archive ouverte HAL Accéder directement au contenu
Communication Dans Un Congrès Année : 2010

Guessing a Conjecture in Enumerative Combinatorics and Proving It with a Computer Algebra System

Résumé

We present a theorem-proving experiment performed with a computer algebra system. It proves a conjecture about the general pattern of the generating functions counting rooted maps of given genus. These functions are characterized by a complex non-linear differential system between generating functions of multi-rooted maps. Establishing a pattern for these functions requires a sophisticated inductive proof. Up to now these proofs were made by hand. This work is the first computer proof of this kind of theorem. Symbolic computations are performed at the same abstraction level as the hand-made proofs, but with a computer algebra system. Generalizing this first success may significantly help solving algebraic problems in enumerative combinatorics.
Fichier principal
Vignette du fichier
giorgetti10_oip.pdf (170.39 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00563330 , version 1 (04-02-2011)

Identifiants

  • HAL Id : hal-00563330 , version 1

Citer

Alain Giorgetti. Guessing a Conjecture in Enumerative Combinatorics and Proving It with a Computer Algebra System. Symbolic Computation in Software Science, Jul 2010, Linz, Austria. pp.5--18. ⟨hal-00563330⟩
161 Consultations
79 Téléchargements

Partager

Gmail Facebook X LinkedIn More