Bijections between affine hyperplane arrangements and valued graphs

Abstract : We show new bijective proofs of previously known formulas for the number of regions of some deformations of the braid arrangement, by means of a bijection between the no-broken-circuit sets of the corresponding integral gain graphs and some kinds of labelled binary trees. This leads to new bijective proofs for the Shi, Catalan, and similar hyperplane arrangements.
Type de document :
Article dans une revue
European Journal of Combinatorics, Elsevier, 2015, Combinatorial geometries: Matroids, oriented matroids and applications. Special issue in memory of Michel Las Vergnas. 50, pp.30-37. 〈10.1016/j.ejc.2015.04.003〉
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01365957
Contributeur : David Forge <>
Soumis le : mardi 13 septembre 2016 - 19:34:46
Dernière modification le : jeudi 15 novembre 2018 - 20:26:57

Lien texte intégral

Identifiants

Citation

David Forge, Sylvie Corteel, Veronique Ventos. Bijections between affine hyperplane arrangements and valued graphs . European Journal of Combinatorics, Elsevier, 2015, Combinatorial geometries: Matroids, oriented matroids and applications. Special issue in memory of Michel Las Vergnas. 50, pp.30-37. 〈10.1016/j.ejc.2015.04.003〉. 〈hal-01365957〉

Partager

Métriques

Consultations de la notice

290