Work

How to stab a polytope

Year: 2024

Type: article

Abstract: We study the set of linear subspaces of a fixed dimension intersecting a given polytope. To describe this set as a semialgebraic subset of a Grassmannian, we introduce a Schubert arrangement of the polytope, defined by the Chow forms of the polytope's faces of complementary dimension. We show that the set of subspaces intersecting a specified family of faces is defined by fixing the sign of the Chow forms of their boundaries. We give inequalities defining the set of stabbing subspaces in terms of sign conditions on the Chow form.

Source: Le Matematiche

DOI: 10.48550/arxiv.2412.00551

Authors: Seemann, Sebastian, Zaffalon, Francesca

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: European Commission, Fonds Wetenschappelijk Onderzoek

Awards: Exploiting combinatorial structures for algebraic and geometric decompositions, The Amplituhedron: Algebra, Combinatorics, and Positive Geometry, Toric Degenerations of Varieties: Theory and Computations., Matroids in Applied and Combinatorial Commutative Algebra, G8284209191

OpenAlex ID: W4405033288

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