Riffle shuffles, cycles, and descents
type: Item
instance of: scholarly article
title: Riffle shuffles, cycles, and descents
zbMATH Open document ID: 0828.05003
DOI: 10.1007/BF01294457
author: Persi Diaconis
author: Michael F. McGrath
author: Jim Pitman
published in: Combinatorica
publication date: 1995-06-08T00:00:00Z
review text: The question of how many times a deck of cards must be shuffled so as to ensure that the resulting distribution of cards corresponds to a draw from the uniform distribution over all permutations of 52 cards has received some attention in the American Press. The present paper continues this line of inquiry. Mathematically, the subject is the study of various kinds of random walks over the permutation group \(S_n\). This paper develops formulae for a variety of functions of permutations resulting from a random walk associated with a repeated riffle shuffle. The main results are obtained by using a bijection theorem of Gessel. The authors provide a self-contained proof of the theorem from first principles.
reviewed by: Rakesh V. Vohra
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 60C05
zbMATH DE Number: 750656
zbMATH Keywords: cycles
zbMATH Keywords: descents
zbMATH Keywords: deck of cards
zbMATH Keywords: permutation group
zbMATH Keywords: permutations
zbMATH Keywords: random walk
zbMATH Keywords: riffle shuffle
zbMATH Keywords: bijection theorem of Gessel
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01294457
OpenAlex ID: W2056940882
description: scientific article; zbMATH DE number 750656