Hypergraph encodings of arbitrary toric ideals

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:166

Article

Petrovic, Sonja¹  Thoma, Apostolos²  Vladoiu, Marius^3,4,5 

[1] IIT, Dept Appl Math, Chicago, IL 60616 USA

[2] Univ Ioannina, Dept Math, GR-45110 Ioannina, Greece

[3] Purdue Univ, Dept Math, 150 N Univ St, W Lafayette, IN 47907 USA

[4] Univ Bucharest, Fac Math & Comp Sci, Str Acad 14, RO-010014 Bucharest, Romania

[5] Romanian Acad, Simion Stoilow Inst Math, POB 1-764, Bucharest 014700, Romania

关键词: Tonic ideals;    Graver basis;    Universal Grobner basis;    Hypergraphs;    Minimal generating sets;    Resolutions;   

DOI  :  10.1016/j.jcta.2019.02.017

来源: Elsevier

【 摘 要 】

Relying on the combinatorial classification of tonic ideals using their bouquet structure, we focus on toric ideals of hypergraphs and study how they relate to general tonic ideals. We show that hypergraphs exhibit a surprisingly general behavior: the tonic ideal associated to any general matrix can be encoded by that of a 0/1 matrix, while preserving the essential combinatorics of the original ideal. We provide two universality results about the unboundedness of degrees of various generating sets: minimal, Graver, universal Grobner bases, and indispensable binomials. Finally, we provide a polarization-type operation for arbitrary positively graded toric ideals, which preserves all the combinatorial signatures and the homological properties of the original tonic ideal. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free