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Toric Ideals of Lattice Path Matroids and Polymatroids

Authors :
Jay Schweig
Publication Year :
2010
Publisher :
arXiv, 2010.

Abstract

We show that the toric ideal of a lattice path polymatroid is generated by quadrics corresponding to symmetric exchanges, and give a monomial order under which these quadrics form a Gr\"obner basis. We then obtain an analogous result for lattice path matroids.<br />Comment: 9 pages, 4 figures

Subjects

Subjects :
Class (set theory)
Algebra and Number Theory
Conjecture
Quadric
Mathematics::Combinatorics
Mathematics::Commutative Algebra
Basis (universal algebra)
Lattice path
Mathematics - Commutative Algebra
Commutative Algebra (math.AC)
Matroid
Combinatorics
Mathematics::Algebraic Geometry
FOS: Mathematics
Mathematics - Combinatorics
Ideal (order theory)
Combinatorics (math.CO)
Monomial order
Mathematics

Details

Database :
OpenAIRE
Accession number :
edsair.doi.dedup.....880b56a85f5b23ab905273c1284e98d4
Full Text :
https://doi.org/10.48550/arxiv.1006.2560
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