Polynomials with only real zeros and the Eulerian polynomials of type D
  A remarkable identity involving the Eulerian polynomials of type D was obtained by Stembridge (Adv. Math. 106 (1994), p. 280, Lemma 9.1). In this paper we explore an equivalent form of this identity. We prove Brenti's real-rootedness conjecture for the Eulerian polynomials of type $D$. 
Shi-Mei Ma
math.CO