Lattice Polytopes with Distinct Pair-Sums

Let P be a lattice polytope in Rn, and let P intersection Zn = {v1,..., vN}. If the N + (N\2) 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 is less than or equal...

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Published inDiscrete & computational geometry Vol. 27; no. 1; pp. 65 - 72
Main Authors Choi, M. D., Lam, T. Y., Reznick, B.
Format Journal Article
LanguageEnglish
Published New York Springer Nature B.V 01.01.2002
Subjects
Computational geometry
Construction
Geometry
Lattice theory
Lattices
Polynomials
Polytopes
Sums
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Summary:Let P be a lattice polytope in Rn, and let P intersection Zn = {v1,..., vN}. If the N + (N\2) 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 is less than or equal to 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. [PUBLICATION ABSTRACT]
Bibliography:ObjectType-Article-1
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ISSN:0179-5376
1432-0444
DOI:10.1007/s00454-001-0052-9