Fractional L-intersecting families

Let L = {a(1)/b(1), . . . , a(s)/b(s)} as bs g, where for every i is an element of [s], a(i)/b(i) is an element of [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 is an element of [m], there exists an a/b is an element of L such that vertical bar A(i) boolean AND A(j)vertical bar is an element of {a/b vertical bar A(i)vertical bar, a/b vertical bar A(j)vertical bar}. In this paper, we introduce and study the notion of fractional L-intersecting families.