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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Kirk Lecture: The mathematics of Shuffling - Cher
yl Praeger (University of Western Australia)
DTSTART;TZID=Europe/London:20200317T160000
DTEND;TZID=Europe/London:20200317T170000
UID:TALK140668AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/140668
DESCRIPTION:The crux of a card trick performed with a deck of
cards usually depends on understanding how shuffle
s of the deck change the order of the cards. By un
derstanding which permutations are possible\, one
knows if a given card may be brought into a certai
n position. The mathematics of shuffling a deck of
2n cards with two ``perfect shuffles'\;'\;
was studied thoroughly by Diaconis\, Graham and Ka
ntor in 1983. I will report on our efforts to unde
rstand a generalisation of this problem\, with a s
o-called "many handed dealer'\;'\; shuffling
kn cards by cutting into k piles with n cards in
each pile and using k! possible shuffles.

A conjecture of Medvedoff and Morrison suggests
that all possible permutations of the deck of card
s are achieved\, as long as k is not 4 and n is no
t a power of k. We confirm this conjecture for thr
ee doubly infinite families of integers\, includin
g all (k\, n) with k >\; n. We initiate a more g
eneral study of shuffle groups\, which admit an ar
bitrary subgroup of shuffles. This is joint work w
ith Carmen Amarra and Luke Morgan.

LOCATION:Seminar Room 1\, Newton Institute
CONTACT:info@newton.ac.uk
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