Generalized laminar families and certain forbidden matrices

2014/06/11 by Peter J. Dukes, Dukes, Peter · 1 citation
Engineering · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1406.3077

openalex publication_date 2014/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Recall that in a laminar family, any two sets are either disjoint or contained one in the other. Here, a parametrized weakening of this condition is introduced. Let us say that a set system F ⊆ 2^X is t-laminar if A,B ∈ F with |A ∩ B| ≥ t implies A ⊆ B or B ⊆ A. We obtain very close asymptotic bounds in terms of n on the maximum size of a 2-laminar family F ⊆ 2^[n]. A construction for 3-laminar families and a crude analysis for general t are also given.

Citations

• The existence of designs

Cited by

• Forbidden Configurations and Boundary Cases

Related

• Upper bounds for the size of set systems with a symmetric set of Hamming distances
• On a generalization of a result of Kleitman
• Upper Bounds For Families Without Weak Delta-Systems
• On transversal and 2-packing numbers in straight line systems on ℝ²
• Set families: restricted distances via restricted intersections