The Lefschetz property for barycentric subdivisions of shellable complexes
| dc.creator | Kubitzke, Martina | |
| dc.creator | Nevo, Eran | |
| dc.date | 2007-12-10 | |
| dc.date.accessioned | 2026-07-07T08:48:22Z | |
| dc.date.available | 2026-07-07T08:48:22Z | |
| dc.description | 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. | |
| dc.description | 16 pages, no figures | |
| dc.identifier | https://arxiv.org/abs/0712.1560 | |
| dc.identifier | http://arxiv.org/abs/0712.1560 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/143921 | |
| dc.subject | Combinatorics | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13F55 | |
| dc.title | The Lefschetz property for barycentric subdivisions of shellable complexes | |
| dc.type | text |