November 11, 2009
Martina Kubitzke (Reykjavík): The Lefschetz property for barycentric subdivisions of shellable complexes
Abstract:
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 Cohen-
Macaulay 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 is verified for barycentric subdivisions of homology
spheres. In addition, using the above algebraic result, we
derive new inequalities on a refinement of the Eulerian statistics
on permutations, where permutations are grouped by the number
of descents and the image of 1.
This is joint work with Eran Nevo.