On Large Systems of Sets with No Large Weak Δ-subsystems

Kostochka, Alexandr; Rödl, Vojtěch

doi:10.1007/pl00009819

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2023

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Cited by 3 publications

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“…4 log log n . The the current best lower bound, due to Kostochka and Rödl [11] (which improved upon [16]), is…”

Section: Introductionmentioning

confidence: 99%

Upper Bounds For Families Without Weak Delta-Systems

Naslund¹

2022

Preprint

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For k ≥ 3, a collection of k sets is said to form a weak ∆-system if the intersection of any two sets from the collection has the same size. Erdős and Szemerédi [8] asked about the size of the largest family F of subsets of {1, . . . , n} that does not contain a weak ∆-system. In this note we improve upon the best upper bound from [13], and show thatn where Θ(C) is the capset capacity. In particular, this shows that

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“…4 log log n . The the current best lower bound, due to Kostochka and Rödl [11] (which improved upon [16]), is…”

Section: Introductionmentioning

confidence: 99%