On Linear Transformations Preserving the Pólya Frequency Property
نویسنده
چکیده
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.
منابع مشابه
On the Existence of Generalized Pólya Frequency Functions Corresponding to Entire Functions with Zeros in Angular Sectors Generalized Pólya Frequency Functions
Generalized Pólya frequency functions are introduced through inverse Mellin transformations of the reciprocals of real entire functions with all zeros in sectors A and −Aφ for 0 ≤ φ ≤ π4 , where A := {z ∈ C | | arg z| ≤ φ}. It is shown that the constant π4 is best possible in this context.
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