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SUMMARY:Cheryl Praeger (University of Western Australia)
DTSTART:20210602T000000Z
DTEND:20210602T010000Z
DTSTAMP:20260422T212711Z
UID:NivenLecture/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NivenLecture
 /1/">Mathematics of Shuffling</a>\nby Cheryl Praeger (University of Wester
 n Australia) as part of Niven lecture\n\n\nAbstract\nThe crux of a card tr
 ick performed with a deck of cards usually depends on understanding how sh
 uffles of the deck change the order of the cards. By understanding which p
 ermutations are possible\, one knows if a given card may be brought into a
  certain position. The mathematics of shuffling a deck of 2n cards with tw
 o ``perfect shuffles'' was studied thoroughly by Diaconis\, Graham and Kan
 tor in 1983. I will report on our efforts to understand a generalisation o
 f this problem\, with a so-called ``many handed dealer'' shuffling kn card
 s 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 possibl
 e permutations of the deck of cards are achieved\, as long as k is not 4 a
 nd n is not a power of k. We confirm this conjecture for three doubly infi
 nite families of integers\, but the conjecture remains open. We initiate a
  more general study of shuffle groups\, which admit an arbitrary subgroup 
 of shuffles. This is joint work with Carmen Amarra and Luke Morgan.\n
LOCATION:https://researchseminars.org/talk/NivenLecture/1/
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