Journal of Combinatorics

Volume 1 (2010)

Number 2

Shuffling with ordered cards

Pages: 121 – 139

DOI: https://dx.doi.org/10.4310/JOC.2010.v1.n2.a3

Authors

Steve Butler (Department of Mathematics, University of California at Los Angeles)

Ron Graham (University of California at San Diego)

Abstract

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 $\order_k(N-q)$.

Keywords

shuffling, ordered cards, posets, periodic, fixed

2010 Mathematics Subject Classification

00A08, 11B75

Published 1 January 2010