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dc.contributor.authorŽivaljević, Radeen
dc.date.accessioned2020-04-12T18:03:57Z-
dc.date.available2020-04-12T18:03:57Z-
dc.date.issued2013-01-01en
dc.identifier.issn0012-365Xen
dc.identifier.urihttp://researchrepository.mi.sanu.ac.rs/handle/123456789/289-
dc.description.abstractWe give an elementary proof of a formula expressing the rotation number of a cyclic unimodular sequence L = u1u2 . . . ud of lattice vectors ui2 in terms of arithmetically defined local quantities. The formula has been originally derived by A. Higashitani and M. Masuda [A. Higashitani, M. Masuda, Lattice multi-polygons, arXiv:1204.0088v2 [math.CO], [v2] Apr 2012; [v3] Dec 2012] with the aid of the Riemann-Roch formula applied in the context of toric topology. These authors also demonstrated that a generalized version of the 'Twelve-point theorem' and a generalized Pick's formula are among the consequences or relatives of their result. Our approach emphasizes the role of 'discrete curvature invariants' μ(a, b, c), where {a, b} and {b, c} are bases of 2, as fundamental discrete invariants of modular lattice geometry.en
dc.publisherElsevier-
dc.relationGeometry and Topology of Manifolds, Classical Mechanics and Integrable Dynamical Systems-
dc.relationTopology, geometry and global analysis on manifolds and discrete structures-
dc.relation.ispartofDiscrete Mathematicsen
dc.subjectLattice points | Rotation number | Toric topology | Unimodular sequenceen
dc.titleRotation number of a unimodular cycle: An elementary approachen
dc.typeArticleen
dc.identifier.doi10.1016/j.disc.2013.06.003en
dc.identifier.scopus2-s2.0-84885172611en
dc.contributor.affiliationMathematical Institute of the Serbian Academy of Sciences and Arts-
dc.relation.firstpage2253en
dc.relation.lastpage2261en
dc.relation.issue20en
dc.relation.volume313en
dc.description.rankM22-
item.cerifentitytypePublications-
item.openairetypeArticle-
item.fulltextNo Fulltext-
item.grantfulltextnone-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
crisitem.author.orcid0000-0001-9801-8839-
crisitem.project.funderMESTD-
crisitem.project.fundingProgramBasic Research (BR or ON)-
crisitem.project.openAireinfo:eu-repo/grantAgreement/MESTD/Basic Research (BR or ON)/174034-
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