Please use this identifier to cite or link to this item: https://scidar.kg.ac.rs/handle/123456789/8390
Title: Polytopal Bier Spheres and Kantorovich–Rubinstein Polytopes of Weighted Cycles
Authors: Jevtić F.
Timotijević, Marinko
Živaljević R.
Issue Date: 2019
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”.
URI: https://scidar.kg.ac.rs/handle/123456789/8390
Type: article
DOI: 10.1007/s00454-019-00151-5
ISSN: 0179-5376
SCOPUS: 2-s2.0-85075376429
Appears in Collections:Faculty of Science, Kragujevac

Page views(s)

116

Downloads(s)

31

Files in This Item:
File Description SizeFormat 
10.1007-s00454-019-00151-5.pdf199.44 kBAdobe PDFThumbnail
View/Open


This item is licensed under a Creative Commons License Creative Commons