Fractional L-intersecting families

2018/03/11 by Balachandran, Niranjan, Mathew, Rogers, Mishra, Tapas Kumar
#05D05 #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics

paper · doi:10.48550/arxiv.1803.03954

Abstract

Let L = \(a₁)/(b₁), … , (a_s)/(b_s)\, where for every i ∈ [s], (a_i)/(b_i) ∈ [0,1) is an irreducible fraction. Let F = \A₁, … , 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.

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