Abstract
Given a polytope P in R d and a subset U of its vertices, is there a triangulation of P using d-simplices that all contain U? We answer this question by proving an equivalent and easy-to-check combinatorial criterion for the facets of P. Our proof relates triangulations of P to triangulations of its “shadow”, a projection to a lower-dimensional space determined by U. In particular, we obtain a formula relating the volume of P with the volume of its shadow. This leads to an exact formula for the volume of a polytope arising in the theory of unit equations.
Originalsprache | englisch |
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Seiten (von - bis) | 69-99 |
Seitenumfang | 31 |
Fachzeitschrift | Publicationes Mathematicae |
Jahrgang | 99 |
Ausgabenummer | 1-2 |
DOIs | |
Publikationsstatus | Veröffentlicht - 2021 |
ASJC Scopus subject areas
- Allgemeine Mathematik
Fields of Expertise
- Information, Communication & Computing