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Annals of Combinatorics

, Volume 6, Issue 3–4, pp 327–335 | Cite as

Lattice Structure and Convergence of a Game of Cards

  • Eric Goles
  • Michel Morvan
  • Ha Duong Phan
Original article

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.

Mathematics Subject Classification2000: 91A46¶Key words and phrases: integer composition, order, lattice, convergence 

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Copyright information

© Birkhäuser Verlag Basel, 2002

Authors and Affiliations

  • Eric Goles
    • 1
  • Michel Morvan
    • 2
  • Ha Duong Phan
    • 3
  1. 1.Departamento de Ingeniería Matemática, Escuela de Ingeniería, Universidad de Chile, Casilla 170-Correo 3, Santiago, Chile, egoles@dim.uchile.clCL
  2. 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
  3. 3.LIAFA, Université Denis Diderot Paris 7, Case 7014-2, Place Jussieu-75256 Paris Cedex, France, phan@liafa.jussieu.frFR

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