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DOI: 10.4230/LIPIcs.SoCG.2017.46
URN: urn:nbn:de:0030-drops-71812
URL: https://drops.dagstuhl.de/opus/volltexte/2017/7181/
Kerber, Michael ; Tichy, Robert ; Weitzer, Mario
Constrained Triangulations, Volumes of Polytopes, and Unit Equations
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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.
BibTeX - Entry
@InProceedings{kerber_et_al:LIPIcs:2017:7181,
author = {Michael Kerber and Robert Tichy and Mario Weitzer},
title = {{Constrained Triangulations, Volumes of Polytopes, and Unit Equations}},
booktitle = {33rd International Symposium on Computational Geometry (SoCG 2017)},
pages = {46:1--46:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-038-5},
ISSN = {1868-8969},
year = {2017},
volume = {77},
editor = {Boris Aronov and Matthew J. Katz},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2017/7181},
URN = {urn:nbn:de:0030-drops-71812},
doi = {10.4230/LIPIcs.SoCG.2017.46},
annote = {Keywords: constrained triangulations, simplotopes, volumes of polytopes, projections of polytopes, unit equations, S-integers}
}
| Keywords: | constrained triangulations, simplotopes, volumes of polytopes, projections of polytopes, unit equations, S-integers | |
| Seminar: | 33rd International Symposium on Computational Geometry (SoCG 2017) | |
| Issue date: | 2017 | |
| Date of publication: | 20.06.2017 |
