Tiling by rectangles and alternating current

M. V. Prasolov, Mikhail Skopenkov

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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. © 2010 Elsevier Inc.
Original languageEnglish (US)
Pages (from-to)920-937
Number of pages18
JournalJournal of Combinatorial Theory, Series A
Volume118
Issue number3
DOIs
StatePublished - Apr 2011

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics
  • Theoretical Computer Science

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