Fractional cross intersecting families

03/05/2019

∙

by   Rogers Mathew, et al.

∙

0

∙

share

Let A={A_1,...,A_p} and B={B_1,...,B_q} be two families of subsets of [n] such that for every i∈ [p] and j∈ [q], |A_i∩ B_j|= c/d|B_j|, where c/d∈ [0,1] is an irreducible fraction. We call such families "c/d-cross intersecting families". In this paper, we find a tight upper bound for the product |A||B| and characterize the cases when this bound is achieved for c/d=1/2. Also, we find a tight upper bound on |A||B| when B is k-uniform and characterize, for all c/d, the cases when this bound is achieved.