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An absorbing
version of the top-to-random shuffle
Joel Brewster Lewis and Mehr Rai |
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Vol. 17 (2024), No. 4, 603–632
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Abstract |
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Consider a randomly shuffled deck of cards with red cards and black cards. We study the average number of moves it takes to go from a randomly shuffled deck to a deck that alternates in color by performing the following move: if the top card and the bottom card of the deck differ in color, place the top card at the bottom of the deck; otherwise, insert the top card randomly in the deck. We use tools from combinatorics, probability, and linear algebra to study this process. |
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Keywords
finite Markov chain, absorbing Markov chain, card
shuffling, top-to-random shuffle
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Mathematical Subject Classification
Primary: 60C05, 60J10
Secondary: 05A05
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Milestones
Received: 16 June 2022
Revised: 2 May 2023
Accepted: 4 May 2023
Published: 2 October 2024
Communicated by Jonathon Peterson
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Authors |
| Joel Brewster Lewis | |
| Department of Mathematics George Washington University Washington, DC United States |
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| Mehr Rai | |
| Department of Mathematics Aalto University FI-00076 Aalto Finland |
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| © 2024 MSP (Mathematical Sciences Publishers). |
