2013/02/04 by Winfried Bruns, Bruns, Winfried
Mathematics · #Advanced Combinatorial Mathematics #Affine transformation #Algebra over a field #Algebraic number #Algebraic structures and combinatorial models #Binomial (polynomial) #Binomial coefficient #Class (philosophy) #Combinatorics #Commutative Algebra and Its Applications #Computer science #Discrete mathematics #Hilbert–Poincaré series #Ideal (ethics) #Mathematics #Normality #Polytope #Prime (order theory) #Prime ideal #Pure mathematics #Ring (chemistry) #Sequence (biology) #Series (stratigraphy) #math.AC #math.CO #msc:13C99 #msc:14M25 #msc:52B20
paper · pdf · doi:10.48550/arxiv.1302.0769
arxiv created 2013/02/04 · openalex publication_date 2013/02/04 · arxiv updated 2013/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recently several authors have proved results on Ehrhart series of free sums of rational polytopes. In this note 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.