BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Cheryl Praeger (University of Western Australia) DTSTART:20210602T000000Z DTEND:20210602T010000Z DTSTAMP:20260404T094341Z UID:NivenLecture/1 DESCRIPTION:Title: Mathematics of Shuffling\nby Cheryl Praeger (University of Western Australia) as part of Niven lecture\n\n\nAbstract\nThe crux of a card trick performed with a deck of cards usually depends on understanding how shuffles of the deck change the order of the cards. By understanding which permutations 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 two ``perfect shuffles'' was studied thoroughly by Diaconis\, Graham and Kantor in 1983. I will report on our efforts to understand a generalis ation of this problem\, with a so-called ``many handed dealer'' shuffling kn cards by cutting into k piles with n cards in each pile and using k! po ssible shuffles. A conjecture of Medvedoff and Morrison suggests that all possible permutations of the deck of cards are achieved\, as long as k is not 4 and n is not a power of k. We confirm this conjecture for three doub ly infinite families of integers\, but the conjecture remains open. We ini tiate a more general study of shuffle groups\, which admit an arbitrary su bgroup of shuffles. This is joint work with Carmen Amarra and Luke Morgan. \n LOCATION:https://stable.researchseminars.org/talk/NivenLecture/1/ END:VEVENT END:VCALENDAR