Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4656123 | Journal of Combinatorial Theory, Series A | 2011 | 18 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics