Lattice polytopes with distinct pair-sums

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dc.creatorChoi, M. D.
dc.creatorLam, T. Y.
dc.creatorReznick, Bruce
dc.date2000-11-10
dc.date.accessioned2026-07-07T04:38:32Z
dc.date.available2026-07-07T04:38:32Z
dc.descriptionLet P be a lattice polytope in R^n, and let P \cap Z^n = {v_1,...,v_N}. If the N + \binom N2 points 2v_1,...,2v_N; v_1+v_2,...v_{N-1}+v_N are distinct, we say that P is a "distinct pair-sum" or "dps" polytope. We show that, if P is a dsp polytope in R^n, then N \le 2^n, and, for every n, we construct dps polytopes in R^n which contain 2^n lattice points. We also discuss the relation between dps polytopes and the study of sums of squares of real polynomials.
dc.description8 pages. Submitted to the Special Issue on Geometric Combinatorics of the journal "Discrete and Computational Geometry"
dc.identifierhttps://arxiv.org/abs/math/0011068
dc.identifierhttp://arxiv.org/abs/math/0011068
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/60315
dc.subjectCombinatorics
dc.subject52B20
dc.titleLattice polytopes with distinct pair-sums
dc.typetext

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