Uniform cross-$t$-intersecting families: proving Hirschorn's conjecture up to polynomial factor
Combinatorics
2021-02-23 v1
Abstract
We consider a problem of maximizing the product of the sizes of two uniform cross--intersecting families of sets. We show that the value of this maximum is at most polynomially larger (in the size of a ground set) than a quantity conjectured by Hirschorn in 2008. At the same time, we observe that it can be strictly bigger.
Keywords
Cite
@article{arxiv.2102.10277,
title = {Uniform cross-$t$-intersecting families: proving Hirschorn's conjecture up to polynomial factor},
author = {Georgii P. Bulgakov and Alexander Kozachinskiy and Mikhail N. Vyalyi},
journal= {arXiv preprint arXiv:2102.10277},
year = {2021}
}
Comments
14 pages