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.

• Type: Conference
• Year: 2009
• Where: DGCI
• Authors: Olivier Bodini, Thomas Fernique, Eric Rémila
• Keywords: DGCI 2009, Discrete Geometry, Lower Bound, Lozenge Tilings, Simple Combinatorial Value