Betti numbers of toric ideals of graphs: A case study

DOI10.1142/S0219498819502268zbMath1441.13055arXiv1807.02154OpenAlexW3099508929WikidataQ128895364 ScholiaQ128895364MaRDI QIDQ5206057

Johannes Hofscheier, Graham Keiper, Federico Galetto, Miguel Eduardo Uribe Paczka, Craig Kohne, Adam Van Tuyl

Publication date: 17 December 2019

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.02154

zbMATH Keywords

Gröbner basestoric idealsgraphsHilbert seriesgraded Betti numbers

Mathematics Subject Classification ID

Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Syzygies, resolutions, complexes and commutative rings (13D02) Combinatorial aspects of commutative algebra (05E40) Commutative rings defined by binomial ideals, toric rings, etc. (13F65)

Related Items

Geometric vertex decomposition and liaison for toric ideals of graphs, Regularity and multiplicity of toric rings of three-dimensional Ferrers diagrams, Regularity and ℎ-polynomials of toric ideals of graphs, Binomial ideals of domino tilings, Splittings of toric ideals, Betti numbers of toric algebras of certain bipartite graphs, Properties of the toric rings of a chordal bipartite family of graphs

Uses Software

• Macaulay2

Cites Work

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• Bounds on the regularity of toric ideals of graphs
• Ehrhart series, unimodality, and integrally closed reflexive polytopes
• Graded syzygies
• Minimal generators of toric ideals of graphs
• Square-free Gröbner degenerations
• Koszul bipartite graphs
• Resolutions by mapping cones
• Bipartite graphs whose edge algebras are complete intersections
• Toric ideals associated with gap-free graphs
• Multiplicities of edge subrings
• Unimodality problems in Ehrhart theory
• Depth of edge rings arising from finite graphs
• Graded Betti numbers of ideals with linear quotients
• Monomial and toric ideals associated to Ferrers graphs
• Algebraic properties of toric rings of graphs
• Rees algebras of edge ideals
• Depth of Initial Ideals of Normal Edge Rings
• Rings of Invariants of Tori, Cohen-Macaulay Rings Generated by Monomials, and Polytopes