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dc.contributor.authorŽunić, Jovišaen
dc.date.accessioned2020-05-01T20:29:01Z-
dc.date.available2020-05-01T20:29:01Z-
dc.date.issued2002-12-28en
dc.identifier.issn0012-365Xen
dc.identifier.urihttp://researchrepository.mi.sanu.ac.rs/handle/123456789/1952-
dc.description.abstractThis paper expresses the minimal possible lp-perimeter of a convex lattice polygon with respect to its number of vertices, where p is an arbitrary integer or p = ∞. It will be shown that such a number, denoted by sp(n), has n3/2 as the order of magnitude for any choice of p. Moreover, sp(n) = 2π/√54Apn3/2 + (n), where n is the number of vertices, Ap equals the area of planar shape \x\p + \y\p < 1, and p is an integer greater than 1. A consequence of the previous result is the solution of the inverse problem. It is shown that Np(s)=33√Ap/3√2π2s2/3 + (s1/3) equals the maximal possible number of vertices of a convex lattice polygon whose lp-perimeter is equal to s. The latter result in a particular case p=2 follows from a well known Jarnik's result. The method used cannot be applied directly to the cases p = 1 and ∞. A slight modification is necessary. In the obtained results the leading terms are in accordance with the above formulas (A1 =2 and A∞ =4), while the rest terms in the expressions for sp(n) and Np(s) are replaced with (n log n) and (s1/3 logs), respectively.en
dc.publisherElsevier-
dc.relation.ispartofDiscrete Mathematicsen
dc.subjectCombinatorial optimization | Convex lattice polygonen
dc.titleExtremal problems on convex lattice polygons in sense of lp-metricsen
dc.typeArticleen
dc.identifier.doi10.1016/S0012-365X(02)00384-9en
dc.identifier.scopus2-s2.0-31244438236en
dc.contributor.affiliationMathematical Institute of the Serbian Academy of Sciences and Arts-
dc.relation.firstpage237en
dc.relation.lastpage250en
dc.relation.issue1-3en
dc.relation.volume259en
dc.description.rankM22-
item.cerifentitytypePublications-
item.openairetypeArticle-
item.fulltextNo Fulltext-
item.grantfulltextnone-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
crisitem.author.orcid0000-0002-1271-4153-

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