On the Real-Rootedness of the Descent Polynomials of $(n-2)$-Stack Sortable Permutations
Keywords:
Eulerian polynomials, descent polynomials, $t$-stack sortable permutations, real-rootedness, interlacing, compatibility.
Abstract
Bóna conjectured that the descent polynomials on $(n-2)$-stack sortable permutations have only real zeros. Brändén proved this conjecture by establishing a more general result. In this paper, we give another proof of Brändén's result by using the theory of $s$-Eulerian polynomials recently developed by Savage and Visontai.