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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
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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, ⟨10.46298/dmtcs.2321⟩. ⟨hal-01229739⟩

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