10.4230/LIPICS.STACS.2008.1334
Ballier, Alexis
Alexis
Ballier
Durand, Bruno
Bruno
Durand
Jeandal, Emmanuel
Emmanuel
Jeandal
Structural aspects of tilings
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
2008
Article
Tiling
domino
patterns
tiling preorder
tiling structure
Albers, Susanne
Susanne
Albers
Weil, Pascal
Pascal
Weil
2008
2008-02-06
2008-02-06
2008-02-06
en
urn:nbn:de:0030-drops-13343
10.4230/LIPIcs.STACS.2008
978-3-939897-06-4
1868-8969
10.4230/LIPIcs.STACS.2008
LIPIcs, Volume 1, STACS 2008
25th International Symposium on Theoretical Aspects of Computer Science
2013
1
7
61
72
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Albers, Susanne
Susanne
Albers
Weil, Pascal
Pascal
Weil
1868-8969
Leibniz International Proceedings in Informatics (LIPIcs)
2008
1
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
12 pages
269625 bytes
application/pdf
Creative Commons Attribution-NoDerivs 3.0 Unported license
info:eu-repo/semantics/openAccess
In this paper, we study the structure of the set of tilings
produced by any given tile-set. For better understanding this
structure, we address the set of finite patterns that each tiling
contains.
This set of patterns can be analyzed in two different contexts:
the first one is combinatorial and the other topological. These
two approaches have independent merits and, once combined, provide
somehow surprising results.
The particular case where the set of produced tilings is countable
is deeply investigated while we prove that the uncountable case
may have a completely different structure.
We introduce a pattern preorder and also make use of
Cantor-Bendixson rank. Our first main result is that a tile-set
that produces only periodic tilings produces only a finite number
of them. Our second main result exhibits a tiling with exactly
one vector of periodicity in the countable case.
LIPIcs, Vol. 1, 25th International Symposium on Theoretical Aspects of Computer Science, pages 61-72