Journal of Combinatorics
Volume 1 (2010)
Shuffling with ordered cards
Pages: 121 – 139
We consider a problem of shuffling a deck of cards with ordered labels.Namely we split the deck of $N=k^tq$ cards (where $t\geq 1$ is maximal) into $k$equally sized stacks and then take the top card off of each stack and sort themby the order of their labels and add them to the shuffled stack. We show how tofind stacks of cards invariant and periodic under the shuffling. We also show when$\gcd(q,k)=1$ the possible periods of this shuffling are divisors of $\order_k(N-q)$.
shuffling, ordered cards, posets, periodic, fixed
2010 Mathematics Subject Classification