Tiling by rectangles and alternating current

Handle URI:
http://hdl.handle.net/10754/561608
Title:
Tiling by rectangles and alternating current
Authors:
Prasolov, M. V.; Skopenkov, Mikhail
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.
KAUST Department:
Visual Computing Center (VCC)
Publisher:
Elsevier BV
Journal:
Journal of Combinatorial Theory, Series A
Issue Date:
Apr-2011
DOI:
10.1016/j.jcta.2010.11.012
ARXIV:
arXiv:1002.1356
Type:
Article
ISSN:
00973165
Sponsors:
The authors are grateful to A. Akopyan, M. Houston, and B. George for useful discussions. M. Skopenkov was supported in part by INTAS grant 06-1000014-6277, Russian Foundation of Basic Research grant 06-01-72551-NCNIL-a, Moebius Contest Foundation for Young Scientists and Euler Foundation.
Additional Links:
http://arxiv.org/abs/arXiv:1002.1356v1
Appears in Collections:
Articles; Visual Computing Center (VCC)

Full metadata record

DC FieldValue Language
dc.contributor.authorPrasolov, M. V.en
dc.contributor.authorSkopenkov, Mikhailen
dc.date.accessioned2015-08-02T09:15:16Zen
dc.date.available2015-08-02T09:15:16Zen
dc.date.issued2011-04en
dc.identifier.issn00973165en
dc.identifier.doi10.1016/j.jcta.2010.11.012en
dc.identifier.urihttp://hdl.handle.net/10754/561608en
dc.description.abstractThis 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.en
dc.description.sponsorshipThe authors are grateful to A. Akopyan, M. Houston, and B. George for useful discussions. M. Skopenkov was supported in part by INTAS grant 06-1000014-6277, Russian Foundation of Basic Research grant 06-01-72551-NCNIL-a, Moebius Contest Foundation for Young Scientists and Euler Foundation.en
dc.publisherElsevier BVen
dc.relation.urlhttp://arxiv.org/abs/arXiv:1002.1356v1en
dc.subjectAlternating currenten
dc.subjectElectrical networken
dc.subjectOrthogonal polygonen
dc.subjectRectangleen
dc.subjectTilingen
dc.titleTiling by rectangles and alternating currenten
dc.typeArticleen
dc.contributor.departmentVisual Computing Center (VCC)en
dc.identifier.journalJournal of Combinatorial Theory, Series Aen
dc.contributor.institutionMoscow State University, Faculty of Mechanics and Mathematics, Leninskie Gory, 1, GSP-1, Moscow, 119991, Russian Federationen
dc.contributor.institutionInstitute for Information Transmission Problems of the, Russian Academy of Sciences, Bolshoy Karetny per. 19, bld. 1, Moscow, 127994, Russian Federationen
dc.identifier.arxividarXiv:1002.1356en
kaust.authorSkopenkov, Mikhailen
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