On card shuffling, a mathematical menu
type: Item
instance of: scholarly article
title: On card shuffling, a mathematical menu
zbMATH Open document ID: 0953.05001
author: Stephanie Gloor
author: Lorenz Halbeisen
published in: Elemente der Mathematik
publication date: 2000-11-22T00:00:00Z
review text: Disguised as a menu served in three courses the authors give an entertaining and yet rigorous answer to a question posed by \textit{C. Spleiss} in [Elem. Math. 52, p. 137 (1997)] on the number of perfect shuffles of some deck of cards that results in the original state of the deck. Representing the shuffle as a permutation \(\sigma\) and using some elementary divisibility arguments they determine the minimum \(l\) for which \(\sigma^l\) is the identity. As a `dessert' some extremal values of \(l\) are discussed and a connection to an open conjecture of Artin is mentioned. The authors close with the remark that the result is not new but that they presented it in a `tasty' and easy-to-digest form.
reviewed by: Dieter Rautenbach
Mathematics Subject Classification ID: 05A05
Mathematics Subject Classification ID: 11A99
Mathematics Subject Classification ID: 20B99
zbMATH DE Number: 1443354
zbMATH Keywords: perfect shuffle
zbMATH Keywords: deck of cards
zbMATH Keywords: conjecture of Artin
MaRDI profile type: Publication
full work available at URL: s000170050067
OpenAlex ID: W1972380105
DOI: 10.1007/S000170050067
description: scientific article; zbMATH DE number 1443354