Carries, Shuffling and An Amazing Matrix

Mathematics – Combinatorics

Scientific paper

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16 pages

Scientific paper

The number of ``carries'' when $n$ random integers are added forms a Markov
chain [23]. We show that this Markov chain has the same transition matrix as
the descent process when a deck of $n$ cards is repeatedly riffle shuffled.
This gives new results for the statistics of carries and shuffling.

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