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    Tiling by rectangles and alternating current

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    Type
    Article
    Authors
    Prasolov, M. V.
    Skopenkov, Mikhail
    KAUST Department
    Visual Computing Center (VCC)
    Date
    2011-04
    Preprint Posting Date
    2010-02-06
    Permanent link to this record
    http://hdl.handle.net/10754/561608
    
    Metadata
    Show full item record
    Abstract
    This paper is on tilings of polygons by rectangles. A celebrated physical interpretation of such tilings by R.L. Brooks, C.A.B. Smith, A.H. Stone and W.T. Tutte uses direct-current circuits. The new approach of this 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 those of C. Freiling, R. Kenyon, M. Laczkovich, D. Rinne, and G. Szekeres. © 2010 Elsevier Inc.
    Sponsors
    The authors are grateful to A. Akopyan, M. Houston, and B. George for useful discussions. M. Skopenkov was supported in part by INTAS grant 06-1000014-6277, Russian Foundation of Basic Research grant 06-01-72551-NCNIL-a, Moebius Contest Foundation for Young Scientists and Euler Foundation.
    Publisher
    Elsevier BV
    Journal
    Journal of Combinatorial Theory, Series A
    DOI
    10.1016/j.jcta.2010.11.012
    arXiv
    1002.1356
    Additional Links
    http://arxiv.org/abs/arXiv:1002.1356v1
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.jcta.2010.11.012
    Scopus Count
    Collections
    Articles; Visual Computing Center (VCC)

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