2026-07-21T19:19:06Z https://drops.dagstuhl.de/oai

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Constrained Triangulations, Volumes of Polytopes, and Unit Equations Kerber, Michael Tichy, Robert Weitzer, Mario constrained triangulations simplotopes volumes of polytopes projections of polytopes unit equations S-integers 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Michael Kerber and Robert Tichy and Mario Weitzer 2017 Is Part Of LIPIcs, Volume 77, 33rd International Symposium on Computational Geometry (SoCG 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SoCG.2017.46 urn:nbn:de:0030-drops-71812 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2017.46 eng https://creativecommons.org/licenses/by/3.0/legalcode