f-Vectors of barycentric subdivisions

By Francesco Brenti, Volkmar Welker. 2006

102 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/951aadfc6ee9060efecba09c8d364720ea3b873d

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In Algebra and Number Theory

1. Petter Brand'en
2. Liam Solus
3. Christos A. Athanasiadis
4. Masahiko Yoshinaga
5. Drew Armstrong
6. Victor Reiner
7. Sergey Fomin
8. David Bessis

In Discrete Mathematics and Combinatorics

1. Liam Solus
2. Petter Brand'en
3. Christos A. Athanasiadis
4. Masahiko Yoshinaga
5. Julius Borcea
6. Drew Armstrong
7. Nathan Reading
8. Victor Reiner

In Geometry and Topology

1. Petter Brand'en
2. Liam Solus
3. Christos A. Athanasiadis
4. Julius Borcea
5. Masahiko Yoshinaga
6. Drew Armstrong

Citations in the corpus

• Symmetric Decompositions and Real-Rootedness (2018, methodology): “luation ϕ. It follows from Theorem 2.6 that Id (hϕ(Z;x)) ≺ hϕ(Z;x). 5. DoublyCohen-Macaulay Level SimplicialComplexes We now use the techniques presented in Section 2 to strengthen some known results [20] on the real-rootedness of h-polynomials of barycentric subdivisions of Boolean complexes when t”
• Gamma-positivity in combinatorics and geometry (2017, background): “arycentric subdivisions of boundary complexes of convex polytopes). For barycentric subdivisions of Boolean complexes which triangulate a sphere, more elementary proofs of Theorem 3.8 can be found in [33, 92]. There is an interesting analog of Theorem 3.8 for triangulations of balls, rather than sph”