Distances on Lozenge Tilings - Archive ouverte HAL Access content directly
Conference Papers Year : 2009

Distances on Lozenge Tilings

Olivier Bodini
Thomas Fernique
  • Function : Author
  • PersonId : 938430
Éric Rémila

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.
Fichier principal
Vignette du fichier
tiling.pdf (530.23 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

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

Identifiers

Cite

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⟩
322 View
191 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More