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.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: 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.
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics
- Theoretical Computer Science