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dc.contributor.authorTurner, Paxton
dc.contributor.authorWu, Yuhuai
dc.date.accessioned2021-01-13T19:20:27Z
dc.date.available2021-01-13T19:20:27Z
dc.date.issued2020-06
dc.date.submitted2020-02
dc.identifier.issn0179-5376
dc.identifier.issn1432-0444
dc.identifier.urihttps://hdl.handle.net/1721.1/129408
dc.description.abstractMotivated by questions from Ehrhart theory, we present new results on discrete equidecomposability. Two rational polygons P and Q are said to be discretely equidecomposable if there exists a piecewise affine-unimodular bijection (equivalently, a piecewise affine-linear bijection that preserves the integer lattice Z²) from P to Q. We develop an invariant for a particular version of this notion called rational finite discrete equidecomposability. We construct triangles that are Ehrhart equivalent but not rationally finitely discretely equidecomposable, thus providing a partial negative answer to a question of Haase–McAllister on whether Ehrhart equivalence implies discrete equidecomposability. Surprisingly, if we delete an edge from each of these triangles, there exists an infinite rational discrete equidecomposability relation between them. Our final section addresses the topic of infinite equidecomposability with concrete examples and a potential setting for further investigation of this phenomenon.en_US
dc.publisherSpringer Science and Business Media LLCen_US
dc.relation.isversionofhttp://dx.doi.org/10.1007/s00454-020-00211-1en_US
dc.rightsArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.en_US
dc.sourceSpringer USen_US
dc.titleDiscrete Equidecomposability and Ehrhart Theory of Polygonsen_US
dc.typeArticleen_US
dc.identifier.citationTurner, Paxton and Yuhuai Wu. "Discrete Equidecomposability and Ehrhart Theory of Polygons." Discrete & Computational Geometry 65, 1 (June 2020): 90–115 © 2020 Springer Science Business Mediaen_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematicsen_US
dc.relation.journalDiscrete & Computational Geometryen_US
dc.eprint.versionAuthor's final manuscripten_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dc.date.updated2021-01-04T04:10:47Z
dc.language.rfc3066en
dc.rights.holderSpringer Science+Business Media, LLC, part of Springer Nature
dspace.embargo.termsY
dspace.date.submission2021-01-04T04:10:46Z
mit.journal.volume65en_US
mit.journal.issue1en_US
mit.licensePUBLISHER_CC


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