Roots of Descent Polynomials and an Algebraic Inequality on Hook Lengths
Roots of Descent Polynomials and an Algebraic Inequality on Hook Lengths
复制标题
下降多项式的根和钩长度的代数不等式
DOI：
10.37236/10753
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
T. McConville
中科院分区：
文献类型：
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作者：
Pakawut Jiradilok;T. McConville
通过将下降多项式重新解释为枚举带状形状的标准Young tableaux的函数，我们使用Naruse的钩长公式将下降多项式表示为两个多项式的乘积：一个是平凡部分，其是线性因子的乘积，另一个来自Naruse公式的激发因子。我们扩大的激励因素积极的牛顿基础上自然产生的成濑的公式。在这种展开式下，每个系数都是某个组合对象的权重，本文引入了这个权重。我们介绍并证明了“切片和推不等式”，比较这样的组合对象的权重。因此，我们建立了一个猜想的证明迪亚兹-洛佩兹等人。下降多项式的根的界限。
By reinterpreting the descent polynomial as a function enumerating standard Young tableaux of a ribbon shape, we use Naruse's hook-length formula to express the descent polynomial as a product of two polynomials: one is a trivial part which is a product of linear factors, and the other comes from the excitation factor of Naruse's formula. We expand the excitation factor positively in a Newton basis which arises naturally from Naruse's formula. Under this expansion, each coefficient is the weight of a certain combinatorial object, which we introduce in this paper. We introduce and prove the "Slice and Push Inequality", which compares the weights of such combinatorial objects. As a consequence, we establish a proof of a conjecture by Diaz-Lopez et al. that bounds the roots of descent polynomials.
DOI：
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发表时间：
2008
期刊：
影响因子：
--
作者：
T.;Ohtsuka;Takeshi Ikeda;池田 岳;池田 岳
通讯作者：
池田 岳