Domino tilings and related models: space of configurations of domains with holes

Authors:
Sébastien Desreux;Martin Matamala;Ivan Rapaport;Eric Rémila
Affiliations:
Laboratoire d'Informatique Algorithmique: Fondements et Applications, UMR 7089 CNRS Univ. Paris 7, 2 place Jussieu, 75251 Paris Cedex 05, France;Departamento de Ingenieria Matematica, Centro de Modelamiento Matematico, UMR 2071 CNRS-Univ. Chile, Blanco Encalada 2120, Santiago, Chile;Departamento de Ingenieria Matematica, Centro de Modelamiento Matematico, UMR 2071 CNRS-Univ. Chile, Blanco Encalada 2120, Santiago, Chile;Laboratoire de l'Informatique du Parallélisme, UMR 5668 CNRS-INRIA-ENS Lyon-Univ. Lyon 1, Cedex 07, France and Groupe de Recherche en Informatique et Mathématiques Appliquées, IUT R ...
Venue:
Theoretical Computer Science - Combinatorics of the discrete plane and tilings
Year:
2004

Citing 9
Cited 1

Tiling with Polyominoes and Combinatorial Group Theory

Journal of Combinatorial Theory Series A
Conway's tiling groups

American Mathematical Monthly
Exact sampling with coupled Markov chains and applications to statistical mechanics

Proceedings of the seventh international conference on Random structures and algorithms
Tiling groups for Wang tiles

SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Introduction to Algorithms

Introduction to Algorithms
Markov chain algorithms for planar lattice structures

FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Combinatorics of perfect matchings in plane bipartite graphs and application to tilings

Theoretical Computer Science - Special issue: Tilings of the plane
An O(n log n)-algorithm for finding a domino tiling of a plane picture whose number of holes is bounded

Theoretical Computer Science - Special issue: Tilings of the plane
An algorithm to generate exactly once every tiling with lozenges of a domain

Theoretical Computer Science - Special issue: Tilings of the plane

Planar dimer tilings

CSR'06 Proceedings of the First international computer science conference on Theory and Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

We first prove that the set of domino tilings of a fixed finite figure is a distributive lattice, even in the case when the figure has holes. We then give a geometrical interpretation of the order given by this lattice, using (not necessarily local) transformations called flips.This study allows us to formulate an exhaustive generation algorithm and a uniform random sampling algorithm.We finally extend these results to other types of tilings (calisson tilings, tilings with bicolored Wang tiles).