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SUMMARY:Families of permutations with a forbidden intersection - David Ell
 is (Queen Mary UL)
DTSTART:20181122T143000Z
DTEND:20181122T153000Z
UID:TALK109873@talks.cam.ac.uk
CONTACT:Andrew Thomason
DESCRIPTION:A family of permutations is said to be 't-intersecting' if any
  two permutations in the family agree on at least t points. It is said to 
 be (t-1)-intersection-free if no two permutations in the family agree on e
 xactly t-1 points. Deza and Frankl conjectured in 1977 that a\nt-intersect
 ing family of permutations in S_n can be no larger than a coset of the sta
 biliser of t points\, provided n is large enough depending on t\; this was
  proved by the speaker and independently by Friedgut and Pilpel in 2008. W
 e give a new proof of a stronger statement: namely\, that a (t-1)-intersec
 tion-free family of permutations in S_n can be no larger than a coset of t
 he stabiliser of t points\, provided n is large enough. This can be seen a
 s an analogue for permutations of seminal results of Frankl and Furedi on 
 families of k-element sets. Our proof is partly algebraic and\npartly comb
 inatorial\; it is more 'robust' than the original proofs of the Deza-Frank
 l conjecture\, using a combinatorial 'quasirandomness' argument to avoid m
 any of the algebraic difficulties of the original proofs. Based on joint w
 ork with Noam Lifshitz (Bar Ilan University).\n
LOCATION:MR12
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