Distances on Lozenge Tilings

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Distances on Lozenge Tilings
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 ≤ 4, the flip-distance between two tilings is equal to the Hamming-distance. Conversely, for n ≥ 6, We show that there is some deficient pairs of tilings for which the flip connection needs more flips than the combinatorial lower bound indicates.
Olivier Bodini, Thomas Fernique, Eric Rémil
Added 26 May 2010
Updated 26 May 2010
Type Conference
Year 2009
Where DGCI
Authors Olivier Bodini, Thomas Fernique, Eric Rémila
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