Tiling by rectangles and alternating currentстатья
Статья опубликована в высокорейтинговом журнале
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Дата последнего поиска статьи во внешних источниках: 9 октября 2015 г.
Аннотация: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.