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

 

On linear transformations preserving the Pólya frequency property


Author: Petter Brändén
Journal: Trans. Amer. Math. Soc. 358 (2006), 3697-3716
MSC (2000): Primary 05A15, 26C10; Secondary 05A19, 05A05, 20F55
Published electronically: February 20, 2006
MathSciNet review: 2218995
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Abstract: We prove that certain linear operators preserve the Pólya frequency property and real-rootedness, and apply our results to settle some conjectures and open problems in combinatorics proposed by Bóna, Brenti and Reiner-Welker.


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Additional Information

Petter Brändén
Affiliation: Matematik, Chalmers tekniska högskola och Göteborgs universitet, S-412 96 Göte- borg, Sweden
Address at time of publication: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1043
Email: branden@math.chalmers.se, branden@umich.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-06-03856-6
PII: S 0002-9947(06)03856-6
Received by editor(s): March 22, 2004
Received by editor(s) in revised form: September 14, 2004
Published electronically: February 20, 2006
Additional Notes: This research was financed by the EC’s IHRP Programme, within the Research Training Network “Algebraic Combinatorics in Europe”, grant HPRN-CT-2001-00272, while the author was at Universitá di Roma “Tor Vergata”, Rome, Italy.
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.