Theorems of Carath\'eodory, Minkowski-Weyl, and Gordan up to symmetry
Abstract
In this paper we extend three classical and fundamental results in polyhedral geometry, namely, Carath\'eodory'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.
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