Fibonacci solitaire

Authors:
Alexander Gnedin;Sergei Kerov
Affiliations:
University of Newcastle, United Kingdom;Steklov Mathematical Institute, St. Petersburg, Russia
Venue:
Random Structures & Algorithms
Year:
2002

Citing 3
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Abstract

Fibonacci Solitaire is a combinatorial algorithm which associates with a permutation of [n] = {1,..., n} a partition of [n] into couples and singletons. We study the output configuration when the algorithm is applied to a random permutation, with emphasis on the large n-asymptotics. We show that the set of singletons, properly scaled, resembles a familiar 'stick-breaking' Poisson configuration, whereas the configuration of couples becomes close to uniform.