For fixed m≥3 and c in the range β_m s^{(m-1)/m} to δ_m s, the extremal families avoiding s disjoint sets are the m-subsets of an (mℓ-1)-set union all sets of size at least m+1.
Erdős, A problem on independentr-tuples,Ann
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
fields
math.CO 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
For fixed m≥3 and large s, the extremal families achieving e((m+1)s−ℓ,s) are exactly the P(m,s,ℓ;L) families when 1≤ℓ≤((m+1)/(2m+1)−o(1))s, confirming the Frankl-Kupavskii conjecture in this regime.
citing papers explorer
-
Towards the Erd\H{o}s--Kleitman Problem: from Erd\H{o}s matching conjecture perspective
For fixed m≥3 and c in the range β_m s^{(m-1)/m} to δ_m s, the extremal families avoiding s disjoint sets are the m-subsets of an (mℓ-1)-set union all sets of size at least m+1.
-
A solution to Frankl and Kupavskii's conjecture concerning Erd\H{o}s-Kleitman matching problem
For fixed m≥3 and large s, the extremal families achieving e((m+1)s−ℓ,s) are exactly the P(m,s,ℓ;L) families when 1≤ℓ≤((m+1)/(2m+1)−o(1))s, confirming the Frankl-Kupavskii conjecture in this regime.