Counting Systems with Irrational Basis for Quasicrystals

  • J. P. Gazeau
  • R. Krejcar
Conference paper
Part of the Centre de Physique des Houches book series (LHWINTER, volume 13)


In the quasicrystalline context (see for instance [1–3]), quasilattices can be thought as mathematical discrete sets supporting atomic sites or Bragg peaks beyond a certain intensity. They play the same role as lattices do for crystals. Most of the proposed definitions are of geometrical nature, sticking to crystalline lattice theory through the celebrated Cut and Project method (see [4]), recently renamed model set method [5] or issued from involved packing construction in real space like the generalized dual method [6,7]. More “algebraic” approaches were also initiated, by several authors (see for instance [8,9]). Recent school or workshop proceedings give a comprehensive account of this original interactive field mixing number theory, lattices and experimental physics (see in Refs. [5,10] for instance).


Bragg Peak Fibonacci Number Pisot Number Penrose Tiling Salem Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag France 2000

Authors and Affiliations

  • J. P. Gazeau
    • 1
  • R. Krejcar
    • 2
  1. 1.Laboratoire de Physique Théorique de la Matière CondenséeUniversité Paris 7 — Denis-DiderotParis Cedex 05France
  2. 2.Department of Mathematics, Faculty of Nuclear Sciences and Physical EngineeringCzech Technical UniversityPrague 2Czech Republic

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