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The Lefschetz property for barycentric subdivisions of shellable complexes
Author(s):
Martina
Kubitzke;
Eran
Nevo
Journal:
Trans. Amer. Math. Soc.
361
(2009),
6151-6163.
MSC (2000):
Primary 13F55
Posted:
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  -vector is unimodal, peaks in its middle degree (one of them if the dimension of the complex is even), and that its  -vector is an  -sequence. In particular, the (combinatorial)  -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  .
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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:
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
Posted:
June 24, 2009
Additional Notes:
The first author was supported by DAAD
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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