On the Real-Rootedness of the Descent Polynomials of (n-2)-Stack Sortable Permutations
On the Real-Rootedness of the Descent Polynomials of (n-2)-Stack Sortable Permutations
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DOI：
10.37236/4613
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发表时间：
2014-08
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通讯作者：
Philip B. Zhang
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文献类型：
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作者：
Philip B. Zhang
B ′ ona证明了$（n-2）$-栈可排序排列上的下降多项式只有真实的零点. Br“和”en通过建立一个更一般的结果证明了这个猜想。本文利用Savage和Visontai最近发展的欧拉多项式理论，给出了Br“和”en“结果的另一种证明.
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.