Barycentric subdivisions

f-VECTORS OF BARYCENTRIC SUBDIVISIONS

For a simplicial complex or more generally Boolean cell complex ∆ we study the behavior of the f and h-vector under barycentric subdivision. We show that if ∆ 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 Bool...

The Multiplicity Conjecture for Barycentric Subdivisions

For a simplicial complex ∆ we study the effect of barycentric subdivision on ring theoretic invariants of its StanleyReisner ring. In particular, for Stanley-Reisner rings of barycentric subdivisions we verify a conjecture by Huneke and Herzog & Srinivasan, that relates the multiplicity of a standard graded k-algebra to the product of the maximal shifts in its minimal free resolution up to the ...

On Face Vectors of Barycentric Subdivisions of Manifolds

We study face vectors of barycentric subdivisions of simplicial homology manifolds. Recently, Kubitzke and Nevo proved that the g-vector of the barycentric subdivision of a Cohen–Macaulay simplicial complex is an M -vector, which in particular proves the g-conjecture for barycentric subdivisions of simplicial homology spheres. In this paper, we prove an analogue of this result for Buchsbaum sim...

The Lefschetz Property for Barycentric Subdivisions of Shellable Complexes

We show that an ’almost strong Lefschetz’ property holds for the barycentric subdivision of a shellable complex. From this we conclude that for the barycentric subdivision of a CohenMacaulay complex, the h-vector is unimodal, peaks in its middle degree (one of them if the dimension of the complex is even), and that its g-vector is an M -sequence. In particular, the (combinatorial) g-conjecture ...

Random Walks on Barycentric Subdivisions and the Strichartz Hexacarpet