Theorems of Carathéodory, Minkowski-Weyl, and Gordan up to symmetry

Abstract

In this paper we extend three classical and fundamental results in polyhedral geometry, namely, Carathéodory's theorem, the Minkowski-Weyl theorem, and Gordan's lemma to infinite dimensional spaces, in which considered cones and monoids are invariant under actions of symmetric groups.

21 pages

References in corpus (4)

• Higher Lawrence configurations
• An equivariant Hochster's formula for ${\mathfrak{S}}_n$-invariant monomial ideals
• Invariant chains in algebra and discrete geometry
• Symmetric subvarieties of infinite affine space

Cited by in corpus (2)

• Orbit-finite linear programming
• On monoids up to symmetry