  Binomial-Eulerian polynomials were introduced by Postnikov, Reiner and
Williams. In this paper, properties of the binomial-Eulerian polynomials,
including recurrence relations and generating functions are studied. We present
three constructive proofs of the recurrence relations for binomial-Eulerian
polynomials. Moreover, we give a combinatorial interpretation of the Betti
number of the complement of the k-equal real hyperplane arrangement.
