Fractional L-intersecting families

03/11/2018

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by   Niranjan Balachandran, et al.

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Let L = {a_1/b_1, ... , a_s/b_s}, where for every i ∈ [s], a_i/b_i∈ [0,1) is an irreducible fraction. Let F = {A_1, ... , A_m} be a family of subsets of [n]. We say F is a fractional L-intersecting family if for every distinct i,j ∈ [m], there exists an a/b∈ L such that |A_i ∩ A_j| ∈{a/b|A_i|, a/b |A_j|}. In this paper, we introduce and study the notion of fractional L-intersecting families.