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# Eulerian polynomials of type $D$ have only real roots

Abstract : We give an intrinsic proof of a conjecture of Brenti that all the roots of the Eulerian polynomial of type $D$ are real and a proof of a conjecture of Dilks, Petersen, and Stembridge that all the roots of the affine Eulerian polynomial of type $B$ are real, as well.
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https://hal.inria.fr/hal-01229739
Contributor : Alain Monteil <>
Submitted on : Tuesday, November 17, 2015 - 10:20:52 AM
Last modification on : Wednesday, August 21, 2019 - 10:38:02 AM
Long-term archiving on: : Friday, April 28, 2017 - 9:23:35 PM

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dmAS0145.pdf
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• HAL Id : hal-01229739, version 1

### Citation

Carla D. Savage, Mirkó Visontai. Eulerian polynomials of type $D$ have only real roots. 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), 2013, Paris, France. pp.527-538. ⟨hal-01229739⟩

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