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arXiv · 1002.1356

Tiling by rectangles and alternating current

M. Prasolov·M. Skopenkov
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Abstract

This paper is on tilings of polygons by rectangles. A celebrated physical interpretation of such tilings due to R.L. Brooks, C.A.B. Smith, A.H. Stone and W.T. Tutte uses direct-current circuits. The new approach of the paper is an application of alternating-current circuits. The following results are obtained: - a necessary condition for a rectangle to be tilable by rectangles of given shapes; - a criterion for a rectangle to be tilable by rectangles similar to it but not all homothetic to it; - a criterion for a generic polygon to be tilable by squares. These results generalize the ones of C. Freiling, R. Kenyon, M. Laczkovich, D. Rinne and G. Szekeres.

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M. Prasolov, M. Skopenkov. 2010-02-06. Tiling by rectangles and alternating current. https://doi.org/10.1016/j.jcta.2010.11.012

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