A remarkable identity involving the Eulerian polynomials of type D wasobtained by Stembridge (Adv. Math. 106 (1994), p. 280, Lemma 9.1). In thispaper we explore an equivalent form of this identity. We prove Brenti'sreal-rootedness conjecture for the Eulerian polynomials of type $D$.
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机译：Stembridge获得了涉及D型欧拉多项式的显着标识（Adv。Math。106（1994），第280页，引理9.1）。在本文中，我们探索了这种身份的等效形式。我们证明了类型$ D $的欧拉多项式的Brenti实根猜想。
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