Forbidden vectorvalued intersections
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 Eoin Long (University of Oxford)
 Thursday 26 January 2017, 14:3015:30
 MR12.
If you have a question about this talk, please contact Andrew Thomason.
Given vectors V = (v_i: i \in [n]) in R^D, we define the Vintersection of A,B \subset [n] to be the vector sum_{i \in A \cap B} v_i. In this talk I will discuss a new, essentially optimal, supersaturation theorem for
Vintersections, which can be roughly stated as saying that any large family of sets contains many pairs (A,B) with Vintersection w, for a wide range of V and w. A famous theorem of Frankl and Rödl corresponds to the
case D=1 and all v_i=1 of our theorem. The case D=2 and v_i=(1,i) solves a conjecture of Kalai.
Joint work with Peter Keevash.
This talk is part of the Combinatorics Seminar series.
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