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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
Stable URL: http://www.jstor.org/stable/40302950
Page Count: 13
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The Lepschetz Property for Barycentric Subdivisions of Shellable Complexes
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Abstract

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.

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