The mathematics of shuffling cards

著者

書誌事項

The mathematics of shuffling cards

Persi Diaconis, Jason Fulman

American Mathematical Society, c2023

  • : [pbk.]

大学図書館所蔵 件 / 全3件

この図書・雑誌をさがす

注記

Includes bibliographical references (p. 321-340) and index

内容説明・目次

内容説明

This book gives a lively development of the mathematics needed to answer the question, ""How many times should a deck of cards be shuffled to mix it up?"" The shuffles studied are the usual ones that real people use: riffle, overhand, and smooshing cards around on the table. The mathematics ranges from probability (Markov chains) to combinatorics (symmetric function theory) to algebra (Hopf algebras). There are applications to magic tricks and gambling along with a careful comparison of the mathematics to the results of real people shuffling real cards. The book explores links between shuffling and higher mathematics--Lie theory, algebraic topology, the geometry of hyperplane arrangements, stochastic calculus, number theory, and more. It offers a useful springboard for seeing how probability theory is applied and leads to many corners of advanced mathematics. The book can serve as a text for an upper division course in mathematics, statistics, or computer science departments and will be appreciated by graduate students and researchers in mathematics, statistics, and computer science, as well as magicians and people with a strong background in mathematics who are interested in games that use playing cards.

目次

Shuffling cards: An introduction Practice and history of shuffling cards Convergence rates for riffle shuffles Features Eigenvectors and Hopf algebras Shuffling and carries Different models for riffle shuffling Move to front shuffling and variations Shuffling and geometry Shuffling and algebraic topology Type B shuffles and shelf shuffling machines Descent algebras, $P$-partitions, and quasisymmetric functions Overhand shuffling ``Smoosh'' shuffle How to shuffle perfectly (randomly) Applications to magic tricks, traffic merging, and statistics Shuffling and multiple zeta values Bibliography Index

「Nielsen BookData」 より

詳細情報

ページトップへ