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Conference papers

Distances on Lozenge Tilings

Olivier Bodini 1 Thomas Fernique 2 Éric Rémila 3
1 APR - Algorithmes, Programmes et Résolution
LIP6 - Laboratoire d'Informatique de Paris 6
2 ARITH - Arithmétique informatique
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : 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 flipdistance (i.e. the number of necessary local transformations involving three lozenges) between two given tilings. It is here proven that, for n<5, the flip-distance between two tilings is equal to the Hamming-distance. Conversely, for n>5, We show that there is some deficient pairs of tilings for which the flip connection needs more flips than the combinatorial lower bound indicates.
keyword : tiling
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Submitted on : Saturday, November 14, 2009 - 9:21:47 PM
Last modification on : Tuesday, November 16, 2021 - 4:39:47 AM
Long-term archiving on: : Thursday, June 17, 2010 - 8:22:45 PM

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Olivier Bodini, Thomas Fernique, Éric Rémila. Distances on Lozenge Tilings. DGCI 2009 - 15th IAPR International Conference on Discrete Geometry for Computer Imagery, Sep 2009, Montreal, Canada. pp.240-251, ⟨10.1007/978-3-642-04397-0_21⟩. ⟨hal-00432218⟩

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