On the Number of p4-Tilings by an n-Omino
2019 ◽
Vol 29
(01)
◽
pp. 3-19
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 [Formula: see text]-omino (i.e., polyomino consisting of [Formula: see text] 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 [Formula: see text]). The proof relies on the analysis of the factorization of the boundary word of a polyomino. We also show an example of a polyomino that has three non-equivalent p4-tilings.
1988 ◽
Vol 62
(03)
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pp. 411-419
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1967 ◽
Vol 28
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pp. 207-244
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1967 ◽
Vol 28
◽
pp. 177-206
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1999 ◽
Vol 173
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pp. 249-254
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1976 ◽
Vol 32
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pp. 577-588
1971 ◽
Vol 29
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pp. 244-245
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