Critical Connectedness of Thin Arithmetical Discrete Planes

  • Valérie Berthé
  • Damien Jamet
  • Timo Jolivet
  • Xavier Provençal
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7749)


The critical thickness of an arithmetical discrete plane refers to the infimum thickness that preserves its 2-connectedness. This infimum thickness can be computed thanks to a multidimensional continued fraction algorithm, namely the fully subtractive algorithm. We provide a characterization of the discrete planes with critical thickness that contain the origin and that are 2-connected.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Valérie Berthé
    • 1
  • Damien Jamet
    • 2
  • Timo Jolivet
    • 1
    • 3
  • Xavier Provençal
    • 4
  1. 1.LIAFA CNRSUniversité Paris DiderotFrance
  2. 2.LORIAUniversité de LorraineFrance
  3. 3.FUNDIM, Department of MathematicsUniversity of TurkuFinland
  4. 4.LAMAUniversité de SavoieFrance

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