$f$-Vectors of Barycentric Subdivisions
| dc.creator | Brenti, Francesco | |
| dc.creator | Welker, Volkmar | |
| dc.date | 2006-06-15 | |
| dc.date.accessioned | 2026-07-07T07:17:18Z | |
| dc.date.available | 2026-07-07T07:17:18Z | |
| dc.description | 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. 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 $d$. | |
| dc.identifier | https://arxiv.org/abs/math/0606356 | |
| dc.identifier | http://arxiv.org/abs/math/0606356 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/113895 | |
| dc.subject | Combinatorics | |
| dc.subject | Algebraic Topology | |
| dc.subject | 05e99, 52c99 | |
| dc.title | $f$-Vectors of Barycentric Subdivisions | |
| dc.type | text |