2018/07/08 by Winfried Bruns, Bruns, Winfried, Bogdan Ichim +1
Economics, Econometrics and Finance · Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #Game Theory and Voting Systems #Metric Geometry (math.MG) #Random Matrices and Applications #math.AC #math.CO #math.MG
paper · pdf · doi:10.48550/arxiv.1807.02835
openalex publication_date 2018/07/08 · arxiv created 2020/11/05 · arxiv updated 2020/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We describe the computation of polytope volumes by descent in the face lattice, its implementation in Normaliz, and the connection to reverse-lexicographic triangulations. The efficiency of the algorithm is demonstrated by several high dimensional polytopes of different characteristics. Finally, we present an application to voting theory where polytope volumes appear as probabilities of certain paradoxa.