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dc.contributor.authorDalfó, Cristina
dc.contributor.authorFiol, Miguel Angel
dc.contributor.authorLópez Lorenzo, Ignacio
dc.contributor.authorMartínez Pérez, Álvaro
dc.date.accessioned2021-04-13T07:45:47Z
dc.date.issued2021-06
dc.identifier.issn0012-365X
dc.identifier.urihttp://hdl.handle.net/10459.1/71007
dc.description.abstractIn this paper, we deal with a simple geometric problem: Is it possible to partition a rectangle into k non-congruent rectangles of equal area? This problem is motivated by the so-called 'Mondrian art problem' that asks a similar question for dissections with rectangles of integer sides. Here, we generalize the Mondrian problem by allowing rectangles of real sides. In this case, we show that the minimum value of k for a rectangle to have a 'perfect Mondrian partition' (that is, with non-congruent equal-area rectangles) is seven. Moreover, we prove that such a partition is unique (up to symmetries) and that there exist exactly two proper perfect Mondrian partitions for k=8. Finally, we also prove that any square has a perfect Mondrian decomposition for k >= 7.
dc.description.sponsorshipThe research of the first author has also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 734922.
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherElsevier
dc.relation.isformatofVersió postprint del document publicat a: https://doi.org/10.1016/j.disc.2021.112389
dc.relation.ispartofDiscrete Mathematics, 2021, vol. 344, num. 6, p. 112389
dc.rightscc-by-nc-nd (c) Elsevier, 2021
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es
dc.subjectMondrian problem
dc.subjectNon-congruent rectangles
dc.subjectDissection
dc.subjectDigraph
dc.titleDecompositions of a rectangle into non-congruent rectangles of equal area
dc.typeinfo:eu-repo/semantics/article
dc.date.updated2021-04-13T07:45:48Z
dc.identifier.idgrec031155
dc.type.versioninfo:eu-repo/semantics/acceptedVersion
dc.rights.accessRightsinfo:eu-repo/semantics/embargoedAccess
dc.identifier.doihttps://doi.org/10.1016/j.disc.2021.112389
dc.relation.projectIDinfo:eu-repo/grantAgreement/EC/H2020/734922/EU/CONNECT
dc.date.embargoEndDate2023-05-31


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cc-by-nc-nd (c) Elsevier, 2021
Except where otherwise noted, this item's license is described as cc-by-nc-nd (c) Elsevier, 2021