A generalization of the Erd\H{o}s-Ko-Rado Theorem
Combinatorics
2015-12-21 v2
Abstract
Our main result is a new upper bound for the size of k-uniform, L-intersecting families of sets, where L contains only positive integers. We characterize extremal families in this setting. Our proof is based on the Ray-Chaudhuri--Wilson Theorem. As an application, we give a new proof for the Erd\H{o}s-Ko-Rado Theorem, improve Fisher's inequality in the uniform case and give an uniform version of the Frankl-F\"uredi conjecture .
Keywords
Cite
@article{arxiv.1512.05531,
title = {A generalization of the Erd\H{o}s-Ko-Rado Theorem},
author = {Gábor Hegedüs},
journal= {arXiv preprint arXiv:1512.05531},
year = {2015}
}
Comments
11 pages