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

Philip B. Zhang

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.


Keywords


Eulerian polynomials; descent polynomials; $t$-stack sortable permutations; real-rootedness; interlacing; compatibility.

Full Text: PDF