On the Real-rootedness of the Descent Polynomials of $(n-2)$-Stack Sortable Permutations

Abstract

B\'ona conjectured that the descent polynomials on $(n-2)$-stack sortable permutations have only real zeros. Br\"and\'en proved this conjecture by establishing a more general result. In this paper, we give another proof of Br\"and\'en's result by using the theory of $s$-Eulerian polynomials recently developed by Savage and Visontai.