Matroid Toric Ideals: Complete Intersection, Minors, and Minimal Systems of Generators - CNRS - Centre national de la recherche scientifique Accéder directement au contenu
Article Dans Une Revue SIAM Journal on Discrete Mathematics Année : 2015

Matroid Toric Ideals: Complete Intersection, Minors, and Minimal Systems of Generators

Résumé

In this paper, we investigate three problems concerning the toric ideal associated to a matroid. Firstly, we list all matroids M such that its corresponding toric ideal I M is a complete intersection. Secondly, we handle the problem of detecting minors of a matroid M from a minimal set of binomial generators of I M. In particular, given a minimal set of binomial generators of I M we provide a necessary condition for M to have a minor isomorphic to U d,2d for d ≥ 2. This condition is proved to be sufficient for d = 2 (leading to a criterion for determining whether M is binary) and for d = 3. Finally, we characterize all matroids M such that I M has a unique minimal set of binomial generators.
Fichier principal
Vignette du fichier
Toric-Ideal-matroids.pdf (111.93 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02049103 , version 1 (26-02-2019)

Identifiants

Citer

Ignacio García-Marco, Jorge Luis Ramírez Alfonsín. Matroid Toric Ideals: Complete Intersection, Minors, and Minimal Systems of Generators. SIAM Journal on Discrete Mathematics, 2015, 29 (4), pp.2267-2276. ⟨10.1137/140986608⟩. ⟨hal-02049103⟩
32 Consultations
76 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More