volume 27, issue 1, P65-72 2002
DOI: 10.1007/s00454-001-0052-9
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Abstract: Abstract. Let P be a lattice polytope in R n , and let P ∩ Z n = {v 1 , . . . , v N }. If the N + N 2 points 2v 1 , . . . , 2v N ; v 1 + v 2 , . . . , v N −1 + v N are distinct, we say that P is a "distinct pairsum" or "dps" polytope. We show that if P is a dps polytope in R n , then N ≤ 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.Let P be a lattice polytope i…

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