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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The Lefschetz property for barycentric subdivisions of shellable complexes


Authors: Martina Kubitzke and Eran Nevo
Journal: Trans. Amer. Math. Soc. 361 (2009), 6151-6163
MSC (2000): Primary 13F55
Published electronically: June 24, 2009
MathSciNet review: 2529927
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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$.


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Additional Information

Martina Kubitzke
Affiliation: Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, 35032 Marburg, Germany
Email: kubitzke@mathematik.uni-marburg.de

Eran Nevo
Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853
Email: eranevo@math.cornell.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04794-1
PII: S 0002-9947(09)04794-1
Keywords: Barycentric subdivision, Stanley-Reisner ring, Lefschetz, shellable
Received by editor(s): January 25, 2008
Received by editor(s) in revised form: March 18, 2008
Published electronically: June 24, 2009
Additional Notes: The first author was supported by DAAD
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.



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