Lower bound theorems for general polytopes

Title: Lower bound theorems for general polytopes
Creator: Pineda-Villavicencio, Guillermo; Ugon, Julien; Yost, David
Date: 2019
Type: Text; Journal article
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/169270
Identifier: vital:13991
Identifier: https://doi.org/10.1016/j.ejc.2018.12.003
Identifier: ISBN:0195-6698
Abstract: For 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 Grunbaum, 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.
Publisher: Elsevier
Relation: European Journal of Combinatorics Vol. 79, no. (2019), p. 27-45; http://purl.org/au-research/grants/arc/DP180100602
Rights: Open Access
Rights: This metadata is freely available under a CCO license
Subject: 0101 Pure Mathematics; Polytopes; Manifold; Simplicial complexes
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