r-wise fractional L-intersecting family

2019/09/29 by Tapas Kumar Mishra, Mishra, Tapas Kumar
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.1909.13217

openalex publication_date 2019/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 r-wise fractional L-intersecting family if for every distinct i₁,i₂, …,i_r ∈ [m], there exists an (a)/(b) ∈ L such that |A_i1 ∩ A_i2 ∩ … ∩ A_ir| ∈ \ (a)/(b)|A_i1|, (a)/(b) |A_i2|,…, (a)/(b) |A_ir| \. 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 [Niranjan et.al, Fractional L-intersecting families, The Electronic Journal of Combinatorics, 2019].

Related

• Fractional L-intersecting families
• Fractional cross intersecting families
• Maximal fractional cross-intersecting families
• Bounded fractional intersecting families are linear in size
• Modular and fractional L-intersecting families of vector spaces