使用分裂对称化算子的显式计算
Explicit computations with the Divided Symmetrization operator
摘要：
给定一个多变量多项式，有一个相关的对称化（特别是把它变成一个对称函数）。Postinkov已经发现了一个permutohedron的体积作为一个特定的线性型的幂的分割对称化（DS）。本文的主要任务是给出并证明各种多项式的封闭形式DS-公式。我们希望这些结果对这些领域的研究人员有价值。此外，这里使用的证明方法很简单，可以进行更多的类似计算。最后，我们列出了一系列这样的公式。
英文摘要：
Given a multi-variable polynomial, there is an associated divided symmetrization (in particular turning it into a symmetric function). Postinkov has found the volume of a permutohedron as a divided symmetrization (DS) of the power of a certain linear form. The main task in this paper is to exhibit and prove closed form DS-formulas for a variety of polynomials. We hope the results to be valuable and available to the research practitioner in these areas. Also, the methods of proof utilized here are simple and amenable to many more analogous computations. We conclude the paper with a list of such formulas.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
