Shuffling with ordered cards

2010/03/23 by Steve Butler, Butler, Steve, Ron Graham +1
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.1003.4422

14 pages, lots of figures

arxiv created 2010/03/23 · arxiv updated 2010/03/24

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>=1 is maximal) into k equally sized stacks and then take the top card off of each stack and sort them by the order of their labels and add them to the shuffled stack. We show how to find stacks of cards invariant and periodic under the shuffling. We also show when gcd(q,k)=1 the possible periods of this shuffling are all divisors of order_k(N-q).

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