Shuffling with ordered cards

Details Shuffling with ordered cards Shuffling with ordered cards

2010-03-23

arxiv.org/abs/1003.4422v1

Mathematics

Combinatorics

14 pages, lots of figures

Scientific paper

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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