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.
Original language | English |
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Pages (from-to) | 6151-6163 |
Number of pages | 13 |
Journal | Transactions of the American Mathematical Society |
Volume | 361 |
Issue number | 11 |
DOIs | |
State | Published - 1 Nov 2009 |
Externally published | Yes |
Keywords
- Barycentric subdivision
- Lefschetz
- Shellable
- Stanley-Reisner ring
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics