2017/03/01 by Czabarka, Eva, Hurlbert, Glenn, Kamat, Vikram
#05D05 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1703.00494
A starting point in the investigation of intersecting systems of subsets of a finite set is the elementary observation that the size of a family of pairwise intersecting subsets of a finite set [n]=1,...,n, denoted by 2[n], is at most 2n-1, with one of the extremal structures being the family comprised of all subsets of [n] containing a fixed element, called as a star. A longstanding conjecture of Chvátal aims to generalize this simple observation for all downsets of 2[n]. In this note, we prove this conjecture for all downsets where every subset contains at most 3 elements.