Positively oriented matroids are realizable

DOI10.4171/JEMS/680zbMath1358.05045arXiv1310.4159MaRDI QIDQ520737

Federico Ardila, Felipe Rincón, Lauren K. Williams

Publication date: 5 April 2017

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1310.4159

zbMATH Keywords

Grassmannianoriented matroidtotal positivitypositroidMac-Phersonianmatroid polytope

Mathematics Subject Classification ID

Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.) (52B40) Grassmannians, Schubert varieties, flag manifolds (14M15) Combinatorial aspects of matroids and geometric lattices (05B35) Oriented matroids in discrete geometry (52C40)

Related Items

The geometry of geometries: matroid theory, old and new ⋮ Polypositroids ⋮ On two notions of total positivity for partial flag varieties ⋮ Combining realization space models of polytopes ⋮ The positive Grassmannian, the amplituhedron, and cluster algebras ⋮ Sign variation, the Grassmannian, and total positivity ⋮ Wilson loop diagrams and positroids ⋮ Positively hyperbolic varieties, tropicalization, and positroids ⋮ The totally nonnegative Grassmannian is a ball ⋮ The totally nonnegative Grassmannian is a ball ⋮ The positive Dressian equals the positive tropical Grassmannian ⋮ The geometry of gaussoids ⋮ Quotients of uniform positroids

Cites Work

• Positroids and Schubert matroids
• Mod 2 cohomology of combinatorial Grassmannians
• Discrete Morse theory for totally non-negative flag varieties
• An infinite family of minor-minimal nonrealizable 3-chirotopes
• A combinatorial abstraction of linear programming
• Oriented matroids today
• Coxeter matroids. With illustrations by Anna Borovik
• The homotopy type of the matroid Grassmannian
• The Bergman complex of a matroid and phylogenetic trees
• IS THE MISSING AXIOM OF MATROID THEORY LOST FOREVER?
• GRASSMANNIANS AND CLUSTER ALGEBRAS
• Shelling totally nonnegative flag varieties
• The maximum numbers of faces of a convex polytope
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