This analysis uncovers whether the affine semigroup of integer points is finitely generated in convex cones, suggesting ramifications for irrational polyhedral cones.
We study the question whether the affine semigroup of integer points in a convex cone can be finitely generated up to symmetries of the cone. We establish general properties of finite generation up to symmetry, and then concentrate on the case of irrational polyhedral cones.
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Blekherman et al. (2025) studied this question.
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