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

Philip B. Zhang

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

Combinatorics 2016-02-08 v2

Authors: Philip B. Zhang

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.

Keywords

real-rootedness descent polynomials stack sortable permutations s-Eulerian polynomials combinatorics

Cite

@article{arxiv.1408.4235,
  title  = {On the Real-rootedness of the Descent Polynomials of $(n-2)$-Stack Sortable Permutations},
  author = {Philip B. Zhang},
  journal= {arXiv preprint arXiv:1408.4235},
  year   = {2016}
}

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9 pages

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