The Natural Matroid of an Integer Polymatroid

Bonin, Joseph E.; Chun, Carolyn; Fife, Tara

doi:10.1137/22m1521122

SIAM J. Discrete Math.

2023

DOI: 10.1137/22m1521122

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The Natural Matroid of an Integer Polymatroid

Joseph E. Bonin

Carolyn Chun

Tara Fife

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2023

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Intersection Theory of Polymatroids

Eur,

Larson

2023

International Mathematics Research Notices

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Polymatroids are combinatorial abstractions of subspace arrangements in the same way that matroids are combinatorial abstractions of hyperplane arrangements. By introducing augmented Chow rings of polymatroids, modeled after augmented wonderful varieties of subspace arrangements, we generalize several algebro-geometric techniques developed in recent years to study matroids. We show that intersection numbers in the augmented Chow ring of a polymatroid are determined by a matching property known as the Hall–Rado condition, which is new even in the case of matroids.

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Intersection Theory of Polymatroids

Eur,

Larson

2023

International Mathematics Research Notices

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show abstract

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The Natural Matroid of an Integer Polymatroid

Cited by 1 publication

References 24 publications

Intersection Theory of Polymatroids

Intersection Theory of Polymatroids

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