Polytope volume by descent in the face lattice and applications in social choice
| Autor(en): | Bruns, Winfried Ichim, Bogdan |
Stichwörter: | COMPUTATIONS; Computer Science; Computer Science, Software Engineering; EHRHART SERIES; Face lattice; Mathematics; Mathematics, Applied; Operations Research & Management Science; Rational polytope; Triangulation; Volume; Voting theory | Erscheinungsdatum: | 2021 | Herausgeber: | SPRINGER HEIDELBERG | Journal: | MATHEMATICAL PROGRAMMING COMPUTATION | Volumen: | 13 | Ausgabe: | 2 | Startseite: | 415 | Seitenende: | 442 | Zusammenfassung: | 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. |
ISSN: | 18672949 | DOI: | 10.1007/s12532-020-00198-z |
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