Mathematische Zeitschrift

, Volume 259, Issue 4, pp 849–865

f-Vectors of barycentric subdivisions


DOI: 10.1007/s00209-007-0251-z

Cite this article as:
Brenti, F. & Welker, V. Math. Z. (2008) 259: 849. doi:10.1007/s00209-007-0251-z


For a simplicial complex or more generally Boolean cell complex Δ we study the behavior of the f- and h-vector under barycentric subdivision. We show that if Δ has a non-negative h-vector then the h-polynomial of its barycentric subdivision has only simple and real zeros. As a consequence this implies a strong version of the Charney–Davis conjecture for spheres that are the subdivision of a Boolean cell complex or the subdivision of the boundary complex of a simple polytope. For a general (d − 1)-dimensional simplicial complex Δ the h-polynomial of its n-th iterated subdivision shows convergent behavior. More precisely, we show that among the zeros of this h-polynomial there is one converging to infinity and the other d − 1 converge to a set of d − 1 real numbers which only depends on d.


Barycentric subdivision f-Vector Real-rootedness Unimodality 

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversita’ di Roma “Tor Vergata”RomaItaly
  2. 2.Fachbereich Mathematik und InformatikPhilipps-Universität MarburgMarburgGermany

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