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Discrete Math

On regular 3-wise intersecting families

Keith Frankston, Rutgers

Location:  Hill 705
Date & time: Monday, 29 January 2018 at 2:00PM - 3:00PM

Abstract:  Ellis and Narayanan showed, verifying a conjecture of Frankl, that any 3-wise intersecting family of subsets of {1,2,...,n} admitting a transitive automorphism group has cardinality o(2^n), while a construction of Frankl demonstrates that the same conclusion need not hold under the weaker constraint of being regular. Answering a question of Cameron, Frankl and Kantor from 1989, we show that the restriction of admitting a transitive automorphism group may be relaxed significantly: we prove that any 3-wise intersecting family of subsets of {1,2,...,n} that is regular and increasing has cardinality o(2^n).

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