Bounds for entries of γ-vectors of flag homology spheres

Jean Philippe Labbé, Eran Nevo

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3 Scopus citations


We present some enumerative and structural results for ag homology spheres. For a ag homology sphere δ, we show that its γ-vector γδ =(1, γ1, γ2, ...) satisfues: γj =0 for all j γ1, γ2 ≤ (γ12, γγ1 ϵ 0, 1, and γγ1-1 ϵ 0, 1, 2, γ1, supporting a conjecture of Nevo and Petersen. Further we characterize the possible structures for δ in extremal cases. As an application, the techniques used produce infunitely many f-vectors of ag balanced simplicial complexes that are not γ-vectors of ag homology spheres (of any dimension); these are the furst examples of this kind. In addition, we prove a ag analog of Perles' 1970 theorem on k-skeleta of polytopes with "few" vertices, specifucally, the number of combinatorial types of κ-skeleta of ag homology spheres with γ1 ≤ b of any given dimension, is bounded independently of the dimension.

Original languageAmerican English
Pages (from-to)2064-2078
Number of pages15
JournalSIAM Journal on Discrete Mathematics
Issue number3
StatePublished - 2017

Bibliographical note

Publisher Copyright:
© 2017 Society for Industrial and Applied Mathematics.


  • Ag complex
  • Face vectors
  • Homology spheres
  • Simplicial complex


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