Tiling by rectangles and alternating current

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:118

Article

Prasolov, M.¹  Skopenkov, M.^2,3 

[1] Moscow MV Lomonosov State Univ, Fac Mech & Math, Moscow 119991, Russia

[2] Russian Acad Sci, Inst Informat Transmiss Problems, Moscow 127994, Russia

[3] King Abdullah Univ Sci & Technol, Thuwal 239556900, Saudi Arabia

关键词: Tiling;    Rectangle;    Orthogonal polygon;    Alternating current;    Electrical network;   

DOI  :  10.1016/j.jcta.2010.11.012

来源: Elsevier

【 摘 要 】

This paper is on tilings of polygons by rectangles. A celebrated physical interpretation of such things 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. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free