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Deciding multiple tiling by polygons in polynomial time

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Abstract

Suppose P is a symmetric convex polygon in the plane. We give an algorithm, running in polynomial time in the number of sides of the polygon, which decides if P can tile the plane by translations at some level (not necessarily at level one; this is multiple tiling). The main technical contribution is a polynomial time algorithm that selects, if this is possible, for each \(j=1,2,\ldots ,n\) one of two given vectors \(e_j\) or \(\tau _j\) so that the selection spans a discrete additive subgroup.

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Funding

This work was supported by the Hellenic Foundation for Research and Innovation, Project HFRI-FM17-1733 and by Grant No 4725 of the University of Crete.

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Correspondence to Mihail N. Kolountzakis.

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Kolountzakis, M.N. Deciding multiple tiling by polygons in polynomial time. Period Math Hung 83, 32–38 (2021). https://doi.org/10.1007/s10998-020-00361-y

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  • DOI: https://doi.org/10.1007/s10998-020-00361-y

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