Gröbner bases of toric ideals associated with matroids

DOI10.1007/s40306-021-00468-5zbMath1496.13042arXiv2001.11835OpenAlexW4206679084MaRDI QIDQ2080337

Ken-ichi Hayase, Takayuki Hibi, Kazuki Shibata, Koyo Katsuno

Publication date: 7 October 2022

Published in: Acta Mathematica Vietnamica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2001.11835

zbMATH Keywords

toric idealsGröbner bases and matroids

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) Combinatorial aspects of matroids and geometric lattices (05B35) Commutative rings defined by binomial ideals, toric rings, etc. (13F65)

Uses Software

• Macaulay2

Cites Work

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• Toric ideals of lattice path matroids and polymatroids
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• A unique exchange property for bases
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• The toric ideal of a matroid of rank 3 is generated by quadrics
• On the toric ideal of a matroid
• Matroids with nine elements
• Toric ideals of series and parallel connections of matroids
• Gröbner Bases
• Base-sortable matroids and Koszulness of semigroup rings

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