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An optimal bound on the number of moves for open mancala

2015; Elsevier BV; Volume: 338; Issue: 11 Linguagem: Inglês

10.1016/j.disc.2015.04.013

1872-681X

Alessandro Musesti, Maurizio Paolini, Cesco Reale,

Mathematical Dynamics and Fractals

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.