On linear transformations preserving the Pólya frequency property

Brändén, Petter

doi:10.1090/S0002-9947-06-03856-6

On linear transformations preserving the Pólya frequency property
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Trans. Amer. Math. Soc. 358 (2006), 3697-3716 Request permission

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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