LIPIcs.ISAAC.2017.5.pdf
- Filesize: 1.83 MB
- 12 pages
Document
On the Number of p4-Tilings by an n-Omino
Authors
-
Part of:
Volume:
28th International Symposium on Algorithms and Computation (ISAAC 2017)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: International Symposium on Algorithms and Computation (ISAAC) - License:
Creative Commons Attribution 3.0 Unported license
- Publication Date: 2017-12-07
Cite As Get BibTex
Kazuyuki Amano and Yoshinobu Haruyama. On the Number of p4-Tilings by an n-Omino. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 5:1-5:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
https://doi.org/10.4230/LIPIcs.ISAAC.2017.5
Abstract
A plane tiling by the copies of a polyomino is called isohedral if every pair of copies in the tiling has a symmetry of the tiling that maps one copy to the other. We show that, for every $n$-omino (i.e., polyomino consisting of n cells), the number of non-equivalent isohedral tilings generated by 90 degree rotations, so called p4-tilings or quarter-turn tilings, is bounded by a constant (independent of n). The proof relies on the analysis of the factorization of the boundary word of a polyomino.
Subject Classification
Keywords
- polyomino
- plane tiling
- isohedral tiling
- word factorization
Metrics
- Access Statistics
-
Total Accesses (updated on a weekly basis)
0PDF Downloads