|Authors:||Baralić, Đorđe||Affiliations:||Mathematical Institute of the Serbian Academy of Sciences and Arts||Title:||Toric topology of balanced simplicial complexes||First page:||117||Last page:||118||Conference:||International conference on occasion of Victor Buchstaber’s 75th birthday: Algebraic topology, combinatorics and mathematical physics - International Seminar on Toric Topology and Homotopy Theory||Issue Date:||2018||Rank:||M30||ISBN:||978-5-98419-080-0||URL:||http://www.mathnet.ru/ConfLogos/1289/VMB75.pdf||Abstract:||
Stanley introduced in  an important class of simplicialcomplexes that arise often in combinatorics, topology andalgebra so called balanced simplicial complexes. An-dimensionalsimplicial complexKis called balanced if its set of verticescan be splitted intondisjoint subsets such that there is notwo vertices spanning the edge ofKand belonging to the samesubset. One of central questions in combinatorics is descriptionof all integer vectors that may appear as the face vectors ofconvex polytopes. The most celebrated result in this problematicis the famousg-theorem.In the paper  Klee and Novik conjectured a strongerbound concerning the face numbers of balanced simplicialn-polytopes. The conjecture known as the Balanced LowerBound Theorem is proved in [1, Theorem 1.3] (“if” part) andin [2, Theorem 5.8] (“only if” part)..
|Publisher:||Steklov Mathematical Institute of Russian Academy of Sciences||Project:||Geometry and Topology of Manifolds, Classical Mechanics and Integrable Dynamical Systems|
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