Please use this identifier to cite or link to this item: https://scidar.kg.ac.rs/handle/123456789/8390
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dc.rights.licenseopenAccess-
dc.contributor.authorJevtić F.-
dc.contributor.authorTimotijević, Marinko-
dc.contributor.authorŽivaljević R.-
dc.date.accessioned2020-09-19T15:36:49Z-
dc.date.available2020-09-19T15:36:49Z-
dc.date.issued2019-
dc.identifier.issn0179-5376-
dc.identifier.urihttps://scidar.kg.ac.rs/handle/123456789/8390-
dc.description.abstract© 2019, Springer Science+Business Media, LLC, part of Springer Nature. The 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”.-
dc.rightsinfo:eu-repo/semantics/openAccess-
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/-
dc.sourceDiscrete and Computational Geometry-
dc.titlePolytopal Bier Spheres and Kantorovich–Rubinstein Polytopes of Weighted Cycles-
dc.typearticle-
dc.identifier.doi10.1007/s00454-019-00151-5-
dc.identifier.scopus2-s2.0-85075376429-
Appears in Collections:Faculty of Science, Kragujevac

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