An optimal algorithm to generate tilings

2003/01/17 by Desreux, Sébastien, Rémila, Eric · 1 citation
#Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0301188

Abstract

This article builds on Thurston's height functions. His tiling algorithm is reinterpreted using lattice theory and then generalized in order to generate any tiling of a hole-free region. Combined with a natural encoding of tilings by words, this allows the generation of a linear extension of the lattice of the tilings.

Cited by

• A Divide-and-Conquer Tiling Method for the Design of Large Aperiodic Phased Arrays

Related

• The Complexity of Tiling Problems
• A lower bound on forcing numbers based on height functions
• A change-of-coordinates from Geometry to Algebra, applied to Brick Tilings
• Local generation of tilings
• Stones, Bones, and Snakes: Tilability of the hexagonal grid via the double dimer model