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Lattice Structure and Convergence of a Game of Cards

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Abstract.

We study the dynamics of the so-called Game of Cards by using tools developed in the context of discrete dynamical systems. We extend a result of [4] and [10] (the last one in the context of distributed systems) that established a necessary and sufficient condition for the game to converge. We precisely describe the lattice structure of the set of configurations and we state bounds for the convergence time.

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Authors and Affiliations

  1. Departamento de Ingeniería Matemática, Escuela de Ingeniería, Universidad de Chile, Casilla 170-Correo 3, Santiago, Chile, egoles@dim.uchile.cl, , , , , , CL

    Eric Goles

  2. LIAFA, Université Denis Diderot Paris 7 and Institut Universitaire de France, Case 7014-2, Place Jussieu-75256 Paris Cedex, France, morvan@liafa.jussieu.fr , , , , , , FR

    Michel Morvan

  3. LIAFA, Université Denis Diderot Paris 7, Case 7014-2, Place Jussieu-75256 Paris Cedex, France, phan@liafa.jussieu.fr, , , , , , FR

    Ha Duong Phan

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  1. Eric Goles
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  2. Michel Morvan
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  3. Ha Duong Phan
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Goles, E., Morvan, M. & Phan, H. Lattice Structure and Convergence of a Game of Cards. Annals of Combinatorics 6, 327–335 (2002). https://doi.org/10.1007/s000260200007

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  • DOI: https://doi.org/10.1007/s000260200007

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