eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2017-06-20
46:1
46:15
10.4230/LIPIcs.SoCG.2017.46
article
Constrained Triangulations, Volumes of Polytopes, and Unit Equations
Kerber, Michael
Tichy, Robert
Weitzer, Mario
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol077-socg2017/LIPIcs.SoCG.2017.46/LIPIcs.SoCG.2017.46.pdf
constrained triangulations
simplotopes
volumes of polytopes
projections of polytopes
unit equations
S-integers