2018/11/28 by Bai, Yandong, Li, Binlong, Liu, Jiuqiang +1
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1811.11533
Let F be a family of subsets of [n]=\1,…,n\ and let L be a set of nonnegative integers. The family F is L-intersecting if |F∩ F'|∈ L for every two distinct members F,F'\inF; and F is k-uniform if all its members have the same size k. A large variety of problems and results in extremal set theory concern on k-uniform L-intersecting families. Many attentions are paid to finding the maximum size of a family among all k-uniform L-intersecting families with prescribed n,k and L. In this paper, from another point of view, we propose and investigate the problem of estimating the maximum size of a member in a family among all uniform L-intersecting families with size m, here n,m and L are prescribed. Our results aim to find out more precise relations of n,m,k and L.