BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.cam.ac.uk//v3//EN
BEGIN:VTIMEZONE
TZID:Europe/London
BEGIN:DAYLIGHT
TZOFFSETFROM:+0000
TZOFFSETTO:+0100
TZNAME:BST
DTSTART:19700329T010000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0100
TZOFFSETTO:+0000
TZNAME:GMT
DTSTART:19701025T020000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CATEGORIES:Combinatorics Seminar
SUMMARY:Families of permutations with a forbidden intersec
tion - David Ellis (Queen Mary UL)
DTSTART;TZID=Europe/London:20181122T143000
DTEND;TZID=Europe/London:20181122T153000
UID:TALK109873AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/109873
DESCRIPTION:A family of permutations is said to be 't-intersec
ting' if any two permutations in the family agree
on at least t points. It is said to be (t-1)-inter
section-free if no two permutations in the family
agree on exactly t-1 points. Deza and Frankl conje
ctured in 1977 that a\nt-intersecting family of pe
rmutations in S_n can be no larger than a coset of
the stabiliser of t points\, provided n is large
enough depending on t\; this was proved by the spe
aker and independently by Friedgut and Pilpel in 2
008. We give a new proof of a stronger statement:
namely\, that a (t-1)-intersection-free family of
permutations in S_n can be no larger than a coset
of the stabiliser of t points\, provided n is larg
e enough. This can be seen as an analogue for perm
utations of seminal results of Frankl and Furedi o
n families of k-element sets. Our proof is partly
algebraic and\npartly combinatorial\; it is more '
robust' than the original proofs of the Deza-Frank
l conjecture\, using a combinatorial 'quasirandomn
ess' argument to avoid many of the algebraic diffi
culties of the original proofs. Based on joint wor
k with Noam Lifshitz (Bar Ilan University).\n
LOCATION:MR12
CONTACT:Andrew Thomason
END:VEVENT
END:VCALENDAR