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- W2968271954 abstract "The mathematics of shuffling a deck of $2n$ cards with two perfect shuffles was brought into clarity by Diaconis, Graham and Kantor. Here we consider a generalisation 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 $k!$ shuffles. A conjecture of Medvedoff and Morrison suggests that all possible permutations of the deck of cards are achieved, so long as $kneq 4$ and $n$ is not a power of $k$. We confirm this conjecture for three doubly infinite families of integers: all $(k,n)$ with $k>n$; all $(k, n)in { (ell^e, ell^f )mid ell geqslant 2, ell^e>4, f mbox{not a multiple of} e}$; and all $(k,n)$ with $k=2^egeqslant 4$ and $n$ not a power of $2$. We open up a more general study of shuffle groups, which admit an arbitrary subgroup of shuffles." @default.
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- W2968271954 date "2019-08-14" @default.
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- W2968271954 title "Generalised shuffle groups" @default.
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