The identity is the most likely exchange shuffle for large n

Details The identity is the most likely exchange shuffle for large n The identity is the most likely exchange shuffle for large n

2000-10-06

arxiv.org/abs/math/0010066v1

Mathematics

Combinatorics

23+2 pages; 3 figures. Submitted to Aequationes Mathematicae

Scientific paper

Let a deck of n cards be shuffled by successively exchanging the cards in positions 1, 2, ..., n with cards in randomly chosen positions. We show that for n equal to 18 or greater, the identity permutation is the most likely. We prove a surprising symmetry of the resulting distribution on permutations. We also obtain the limiting distribution of the number of fixed points as n goes to infinity.

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