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SUMMARY:Multiply Intersecting Families. - Agnijo Banerjee (Cambridge)
DTSTART:20250522T133000Z
DTEND:20250522T143000Z
UID:TALK232492@talks.cam.ac.uk
CONTACT:103978
DESCRIPTION:A family F ⊂ P(n) is r-wise k-intersecting if |A1 ∩ · · 
 · ∩ Ar| ≥ k for any A1\, . . . \, Ar ∈ F. It is easily seen that if
  F is r-wise k-intersecting for r ≥ 2\, k ≥ 1 then |F| ≤ 2^(n−1) .
  The problem of determining the maximal size of a family F that is both r1
 -wise k1-intersecting and r2-wise k2-intersecting was raised in 2019 by Fr
 ankl and Kupavskii. They proved the surprising result that\, for (r1\, k1)
  = (3\, 1) and (r2\, k2) = (2\, 32) then this maximum is at most 2^(n−2)
  \, and conjectured the same holds if k2 is replaced by 3. In this talk I 
 shall not only prove this conjecture but also determine the exact maximum 
 for (r1\, k1) = (3\, 1) and (r2\, k2) = (2\, 3) for all n.
LOCATION:MR12
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