For the Erdős–Kleitman problem e(ms+c,s), specific families P' are proven extremal for β_m s^{(m-1)/m} ≤ c ≤ δ_m s (m fixed), with a sharpened range for m=3, and a new family R disproves the Kupavskii–Sokolov conjecture in an intermediate range.
Frankl, Proof of the Erdős Matching Conjecture in a new range,Israel J
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New Extremal Ranges and Constructions of the Erd\H{o}s--Kleitman Problem
For the Erdős–Kleitman problem e(ms+c,s), specific families P' are proven extremal for β_m s^{(m-1)/m} ≤ c ≤ δ_m s (m fixed), with a sharpened range for m=3, and a new family R disproves the Kupavskii–Sokolov conjecture in an intermediate range.