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Description: |
When Maurits Cornelis Escher started to produce astonishing tesselations of the plane in the late 30's, very few properties were known about theses. The ``simplest" tessellations make use of just one polygon or tile for tiling the entire plane, and the polygons that tile the plane by translation are characterized by a simple property due to Beauquier and Nivat (1991) stating that the border b(P) of such a polygon may be factorized as b(P) = ABC\hat(A) \hat(B)\hat(C). This equation maybe naturally translated in an equation on words, that led to the discovery of new classes of polyominoes, connected to the Fibonacci sequence and the Pell sequence.
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