On the Number of p4-Tilings by an n-Omino

Amano, Kazuyuki; Haruyama, Yoshinobu

doi:10.4230/LIPIcs.ISAAC.2017.5

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On the Number of p4-Tilings by an n-Omino

Authors Kazuyuki Amano, Yoshinobu Haruyama

Part of: Volume: 28th International Symposium on Algorithms and Computation (ISAAC 2017)
Part of: Series: Leibniz International Proceedings in Informatics (LIPIcs)
Part of: Conference: International Symposium on Algorithms and Computation (ISAAC)
License: Creative Commons Attribution 3.0 Unported license
Publication Date: 2017-12-07

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Document Identifiers

DOI: 10.4230/LIPIcs.ISAAC.2017.5
URN: urn:nbn:de:0030-drops-82498

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Keywords

polyomino
plane tiling
isohedral tiling
word factorization

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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.

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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

Author Details

Kazuyuki Amano

Yoshinobu Haruyama

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