Distances on Lozenge Tilings
Résumé
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.
| Origine | Fichiers produits par l'(les) auteur(s) |
|---|
Loading...