Tiling by rectangles and alternating current期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

Tiling by rectangles and alternating current

Authors:	M Prasolov

Institution:	^a Moscow State University, Faculty of Mechanics and Mathematics, Leninskie Gory, 1, GSP-1, Moscow, 119991, Russian Federation ^b Institute for Information Transmission Problems of the Russian Academy of Sciences, Bolshoy Karetny per. 19, bld. 1, Moscow, 127994, Russian Federation ^c King Abdullah University of Science and Technology, P.O. Box 2187, 4700 KAUST, 23955-6900 Thuwal, Saudi Arabia

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.

Keywords:	Tiling Rectangle Orthogonal polygon Alternating current Electrical network
本文献已被 ScienceDirect 等数据库收录！