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19 août 2011
- handle: 10670/1.ma1u38
- Blondin Massé, Alexandre; Brlek, Srecko; Garon, Ariane et Labbé, Sébastien (2011). « Two infinite families of polyominoes that tile the plane by translation in two distinct ways ». Theoretical Computer Science, 412(36), pp. 4778-4786.
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http://archipel.uqam.ca/8428/
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http://dx.doi.org/10.1016/j.tcs
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doi:10.1016/j.tcs.2010.12.034
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Infinity Sequence, Fibonacci Fibonacci sequence Numbers, Fibonacci Family Family structure Families--Social aspects Families--Social conditions Family life Structure, Family Family relationships Relationships, FamilyCiter ce document
Alexandre Blondin Massé et al., « Two infinite families of polyominoes that tile the plane by translation in two distinct ways », UQAM Archipel : articles scientifiques, ID : 10670/1.ma1u38
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It has been proved that, among the polyominoes that tile the plane by translation, the so-called squares tile the plane in at most two distinct ways. In this paper, we focus on double squares, that is, the polyominoes that tile the plane in exactly two distinct ways. Our approach is based on solving equations on words, which allows us to exhibit properties about their shape. Moreover, we describe two infinite families of double squares. The first one is directly linked to Christoffel words and may be interpreted as segments of thick straight lines. The second one stems from the Fibonacci sequence and reveals some fractal features.