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The degree of point configurations: Ehrhart theory, Tverberg points and almost neighborly polytopes
Stockholm University, Faculty of Science, Department of Mathematics.
Number of Authors: 2
2015 (English)In: European journal of combinatorics (Print), ISSN 0195-6698, E-ISSN 1095-9971, Vol. 50, 159-179 p.Article in journal (Refereed) Published
Abstract [en]

The degree of a point configuration is defined as the maximal codimension of its interior faces. This concept is motivated from a corresponding Ehrhart-theoretic notion for lattice polytopes and is related to neighborly polytopes, to the Generalized Lower Bound Theorem and, by Gale duality, to Tverberg theory. The main results of this paper are a complete classification of point configurations of degree 1, as well as a structure result on point configurations whose degree is less than a third of the dimension. Statements and proofs involve the novel notion of a weak Cayley decomposition, and imply that the m-core of a set S of n points in R-r is contained in the set of Tverberg points of order (3m - 2(n - r)) of S.

Place, publisher, year, edition, pages
2015. Vol. 50, 159-179 p.
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URN: urn:nbn:se:su:diva-119524DOI: 10.1016/j.ejc.2015.03.024ISI: 000357835900015OAI: diva2:847913
Available from: 2015-08-21 Created: 2015-08-17 Last updated: 2015-08-21Bibliographically approved

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