An optimal bound on the number of moves for open mancala

We determine the optimal bound for the maximum number of moves required to reach a periodic configuration of open mancala (also called open owari), inspired by a popular African game. A mancala move can be interpreted as a map from the set of compositions of a given integer in itself, thus relating...

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Bibliographic Details
Published in:Discrete mathematics 2015-11, Vol.338 (11), p.1827-1844
Main Authors: Musesti, Alessandro, Paolini, Maurizio, Reale, Cesco
Format: Article
Language:English
Subjects:
Discrete dynamical system
Discrete-time games
Integer compositions
Zero-player game
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Summary:We determine the optimal bound for the maximum number of moves required to reach a periodic configuration of open mancala (also called open owari), inspired by a popular African game. A mancala move can be interpreted as a map from the set of compositions of a given integer in itself, thus relating our result to the study of the corresponding finite dynamical system.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2015.04.013