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Lower bound theorems for general polytopes
journal contribution
posted on 2019-06-01, 00:00 authored by G Pineda-Villavicencio, Julien UgonJulien Ugon, D YostFor a d-dimensional polytope with v vertices, d+1≤v≤2d, we calculate precisely the minimum possible number of m-dimensional faces, when m=1 or m≥0.62d. This confirms a conjecture of Grünbaum, for these values of m. For v=2d+1, we solve the same problem when m=1 or d−2; the solution was already known for m=d−1. In all these cases, we give a characterisation of the minimising polytopes. We also show that there are many gaps in the possible number of m-faces: for example, there is no polytope with 80 edges in dimension 10, and a polytope with 407 edges can have dimension at most 23.
History
Journal
European journal of combinatoricsVolume
79Pagination
27 - 45Publisher
ElsevierLocation
Amsterdam, The NetherlandsPublisher DOI
ISSN
0195-6698Language
engPublication classification
C1 Refereed article in a scholarly journalCopyright notice
2018, Elsevier Ltd.Usage metrics
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