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The \(\gamma \)-vector of a barycentric subdivision. (English) Zbl 1231.05307

Summary: We prove that the \(\gamma \)-vector of the barycentric subdivision of a simplicial sphere is the \(f\)-vector of a balanced simplicial complex. The combinatorial basis for this work is the study of certain refinements of Eulerian numbers used by Brenti and Welker to describe the \(h\)-vector of the barycentric subdivision of a boolean complex.

MSC:

05E45 Combinatorial aspects of simplicial complexes
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