Lattice Polytopes with Distinct Pair-Sums

• Published in: Discrete & computational geometry Vol. 27; no. 1; pp. 65 - 72
• Main Authors: Choi, M. D., Lam, T. Y., Reznick, B.
• Format: Journal Article
• Language: English
• Published: New York Springer Nature B.V 01.01.2002
• Subjects: Computational geometry; Construction; Geometry; Lattice theory; Lattices; Polynomials; Polytopes; 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...