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dc.contributor.authorVrećica, Sinišaen
dc.contributor.authorŽivaljević, Radeen
dc.date.accessioned2020-04-12T18:03:57Z-
dc.date.available2020-04-12T18:03:57Z-
dc.date.issued2011-08-01en
dc.identifier.issn0021-2172en
dc.identifier.urihttp://researchrepository.mi.sanu.ac.rs/handle/123456789/292-
dc.description.abstractThe cyclohedron Wn, known also as the Bott-Taubes polytope, arises both as the polyhedral realization of the poset of all cyclic bracketings of the word x1x2··· xn and as an essential part of the Fulton-MacPherson compactification of the configuration space of n distinct, labelled points on the circle S1. The "polygonal pegs problem" asks whether every simple, closed curve in the plane or in the higher dimensional space admits an inscribed polygon of a given shape. We develop a new approach to the polygonal pegs problem based on the Fulton-MacPherson (Axelrod-Singer, Kontsevich) compactification of the configuration space of (cyclically) ordered n-element subsets in S1. Among the results obtained by this method are proofs of Grünbaum's conjecture about affine regular hexagons inscribed in smooth Jordan curves and a new proof of the conjecture of Hadwiger about inscribed parallelograms in smooth, simple, closed curves in the 3-space (originally established by Makeev in [Mak]).en
dc.publisherSpringer Link-
dc.relationSupported by Grants 144014 and 144026 of the Serbian Ministry of Science and Technology-
dc.relation.ispartofIsrael Journal of Mathematicsen
dc.titleFulton-MacPherson compactification, cyclohedra, and the polygonal pegs problemen
dc.typeArticleen
dc.identifier.doi10.1007/s11856-011-0066-9en
dc.identifier.scopus2-s2.0-79960984474en
dc.contributor.affiliationMathematical Institute of the Serbian Academy of Sciences and Arts-
dc.relation.firstpage221en
dc.relation.lastpage249en
dc.relation.issue1en
dc.relation.volume184en
dc.description.rankM21-
item.openairetypeArticle-
item.cerifentitytypePublications-
item.fulltextNo Fulltext-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.grantfulltextnone-
crisitem.author.orcid0000-0001-9801-8839-
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