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dc.contributor.authorJevtić, Filipen
dc.contributor.authorTimotijević, Marinkoen
dc.contributor.authorŽivaljević, Radeen
dc.date.accessioned2020-04-12T18:03:55Z-
dc.date.available2020-04-12T18:03:55Z-
dc.date.issued2019-01-01en
dc.identifier.issn0179-5376en
dc.identifier.urihttp://researchrepository.mi.sanu.ac.rs/handle/123456789/275-
dc.description.abstractThe problem of deciding if a given triangulation of a sphere can be realized as the boundary sphere of a simplicial, convex polytope is known as the ‘Simplicial Steinitz problem’. It is known by an indirect and non-constructive argument that a vast majority of Bier spheres are non-polytopal. Contrary to that, we demonstrate that the Bier spheres associated to threshold simplicial complexes are all polytopal. Moreover, we show that all Bier spheres are starshaped. We also establish a connection between Bier spheres and Kantorovich–Rubinstein polytopes by showing that the boundary sphere of the KR-polytope associated to a polygonal linkage (weighted cycle) is isomorphic to the Bier sphere of the associated simplicial complex of “short sets”.en
dc.publisherSpringer Link-
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 and Computational Geometryen
dc.subjectBier spheres | Gale transform | Kantorovich–Rubinstein polytopes | Polygonal linkages | Polyhedral combinatorics | Simplicial Steinitz problemen
dc.titlePolytopal Bier Spheres and Kantorovich–Rubinstein Polytopes of Weighted Cyclesen
dc.typeArticleen
dc.identifier.doi10.1007/s00454-019-00151-5en
dc.identifier.scopus2-s2.0-85075376429en
dc.description.rankM22-
item.cerifentitytypePublications-
item.openairetypeArticle-
item.fulltextNo Fulltext-
item.grantfulltextnone-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
crisitem.author.orcid0009-0009-9594-9895-
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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