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Free sums of polytopes - the algebraic perspectiveAlgebra & Discrete Mathematics
Recently several authors have proved results on Ehrhart series of free sums of rational polytopes. We treat these results from an algebraic viewpoint. Instead of attacking combinatorial statements directly, we derive them from structural results on affine monoids and their algebras that allow conclusions for Hilbert and Ehrhart series. We characterize when a binomial regular sequence generates a prime ideal or even normality is preserved for the residue class ring.