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Abstract
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Card shuffling models have provided simple motivating examples for the
mathematical theory of mixing times for Markov chains. As a complement, we
introduce a more intricate realistic model of a certain observable real-world scheme
for mixing human players onto teams. We quantify numerically the effectiveness of
this mixing scheme over the seven or eight steps performed in practice. We
give a combinatorial proof of the nontrivial fact that the chain is indeed
irreducible.
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Keywords
Markov chain, mixing time, sports
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Mathematical Subject Classification
Primary: 60J10
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Milestones
Received: 26 January 2021
Revised: 29 May 2021
Accepted: 16 June 2021
Published: 9 February 2022
Communicated by Jonathon Peterson
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