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Conference Papers Year : 2009

Distances on Lozenge Tilings

Olivier Bodini
Thomas Fernique
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Éric Rémila


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.
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Dates and versions

hal-00432218 , version 1 (14-11-2009)



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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