Manickam-Mikl\'os-Singhi 猜想的一个新的二次界
组合数学
2014-07-22 v4
摘要
二十五多年前，Manickam、Miklos 和 Singhi 猜想：对于满足 的正整数 ，任何和为非负的 个实数集合中，至少有 个 元子集的和也是非负的。我们在 时验证了这一猜想，这同时改进并简化了 Alon、Huang 和 Sudakov 的界，以及在 时 Pokrovskiy 的界。
引用
@article{arxiv.1403.1844,
title = {A New Quadratic Bound for the Manickam-Mikl\'os-Singhi Conjecture},
author = {Ameera Chowdhury and Ghassan Sarkis and Shahriar Shahriari},
journal= {arXiv preprint arXiv:1403.1844},
year = {2014}
}
备注
10 pages. The arguments here are similar to those in arXiv:1309.2212, where we tackle the Manickam-Miklos-Singhi conjectures for sets and vector spaces simultaneously. For the reader's convenience, we present the calculations for the case of sets in full detail in this unpublished manuscript. Version 4 has an updated bibliography