Lattice polytopes with distinct pair-sums

M. D. Choi, T. Y. Lam, B. Reznick

Research output: Contribution to journalArticlepeer-review


Let P be a lattice polytope in Rn, and let P ∩ Zn = {v1,..., vN}. If the N+ (2N) points 2v1,..., 2vN; v1+v2,..., vN-1 + vN are distinct, we say that P is a "distinct pair-sum" or "dps" polytope. We show that if P is a dps polytope in Rn, then N ≤2n, and, for every n, we construct dps polytopes in Rn which contain 2n lattice points. We also discuss the relation between dps polytopes and the study of sums of squares of real polynomials.

Original languageEnglish (US)
Pages (from-to)65-72
Number of pages8
JournalDiscrete and Computational Geometry
Issue number1
StatePublished - Jan 2002

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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