r-wise fractional L-intersecting family

09/29/2019

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by   Tapas Kumar Mishra, 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 r-wise fractional L-intersecting family if for every distinct i_1,i_2, ...,i_r ∈ [m], there exists an a/b∈ L such that |A_i_1∩ A_i_2∩...∩ A_i_r| ∈{a/b|A_i_1|, a/b |A_i_2|,..., a/b |A_i_r| }. In this paper, we introduce and study the notion of r-wise fractional L-intersecting families. This is a generalization of notion of fractional L-intersecting families studied in <cit.>.