You are not currently logged in.
Access JSTOR through your library or other institution:
If You Use a Screen ReaderThis content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
The Lepschetz Property for Barycentric Subdivisions of Shellable Complexes
Martina Kubitzke and Eran Nevo
Transactions of the American Mathematical Society
Vol. 361, No. 11 (Nov., 2009), pp. 6151-6163
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/40302950
Page Count: 13
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Preview not available
We show that an 'almost strong Lefschetz' property holds for the barycentric subdivision of a shellable complex. Prom this we conclude that for the barycentric subdivision of a Cohen-Macaulay complex, the ft-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) p-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.
Transactions of the American Mathematical Society © 2009 American Mathematical Society