Lattice polytopes with distinct pair-sums
组合数学
2007-05-23 v1
摘要
Let 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.
引用
@article{arxiv.math/0011068,
title = {Lattice polytopes with distinct pair-sums},
author = {M. D. Choi and T. Y. Lam and Bruce Reznick},
journal= {arXiv preprint arXiv:math/0011068},
year = {2007}
}
备注
8 pages. Submitted to the Special Issue on Geometric Combinatorics of the journal "Discrete and Computational Geometry"