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.
Original language | English |
---|---|
Pages (from-to) | 69-99 |
Number of pages | 31 |
Journal | Publicationes Mathematicae |
Volume | 99 |
Issue number | 1-2 |
DOIs | |
Publication status | Published - 2021 |
Keywords
- Constrained triangulations
- Projections of polytopes
- S-integers
- Simplotopes
- Unit equations
- Volumes of polytopes
ASJC Scopus subject areas
- Mathematics(all)
Fields of Expertise
- Information, Communication & Computing