2010/02/28 by Maxim Prasolov, M. Prasolov, Mikhail Skopenkov +1
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Combinatorics #Computer science #Current (fluid) #Discrete mathematics #Geometry #Homothetic transformation #Mathematics #Numerical methods in inverse problems #Physics #Polygon (computer graphics) #Rectangle #Scientific Research and Discoveries #math-ph #math.CO #math.MP #msc:30C15 #msc:31C20 #msc:52C20 #msc:60J10 #msc:94C05
paper · pdf · doi:10.1016/j.jcta.2010.11.012
published as J. Combinatorial Theory, Series A 118:3 (2011) 920-937 · In English and in Russian; 21 pages; 6 figures; minor improvement of exposition, Russian translation added
openalex publication_date 2010/11/19 · arxiv created 2016/06/15 · arxiv updated 2016/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.