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A simple combinatorial proof of a generalization of a result of Polo

Author: Fabrizio Caselli
Journal: Represent. Theory 8 (2004), 479-486
MSC (2000): Primary 05E15, 20C08
Published electronically: November 2, 2004
MathSciNet review: 2110357
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Abstract: We provide a simple combinatorial proof of, and generalize, a theorem of Polo which asserts that for any polynomial $P\in \mathbb N[q]$ such that $P(0)=1$ there exist two permutations $u$ and $v$ in a suitable symmetric group such that $P$ is equal to the Kazhdan-Lusztig polynomial $P^{v}_{u}$.

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Fabrizio Caselli
Affiliation: Università di Roma “La Sapienza”, Dipartimento di matematica “G. Castelnuovo”, P.le A. Moro 3, 00185, Roma, Italy
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Received by editor(s): July 30, 2003
Received by editor(s) in revised form: March 19, 2004, and July 25, 2004
Published electronically: November 2, 2004
Additional Notes: The author was partially supported by EC grant HPRN-CT-2002-00272
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.