Distances on Lozenge Tilings

  • Olivier Bodini
  • Thomas Fernique
  • Éric Rémila
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5810)


In this paper, a structural property of the set of lozenge tilings of a 2n-gon is highlighted. We introduce a simple combinatorial value called Hamming-distance, which is a lower bound for the the number of flips – a local transformation on tilings – necessary to link two tilings. We prove that the flip-distance between two tilings is equal to the Hamming-distance for n ≤ 4. We also show, by providing a pair of so-called deficient tilings, that this does not hold for n ≥ 6. We finally discuss the n = 5 case, which remains open.


Height Function Local Transformation Bruhat Order Penrose Tiling Tiling Space 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Olivier Bodini
    • 1
  • Thomas Fernique
    • 2
  • Éric Rémila
    • 3
  1. 1.LIP6CNRS & Univ. Paris 6ParisFrance
  2. 2.LIFCNRS & Univ. de ProvenceMarseilleFrance
  3. 3.LIPCNRS & Univ. de Lyon 1LyonFrance

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