论文标题
高斯多项式的炒范德尔蒙德卷积
Scrambled Vandermonde Convolutions of Gaussian Polynomials
论文作者
论文摘要
众所周知，高斯多项式（即$ q $ binamials）描述了矩形网格中单调路径上$面积$统计的分布。我们介绍了两个新的统计数据，$ Corners $和$ Cindex $；将``装饰品''附加到网格上；并重新评估了这些统计数据，以指出$ cindex $统计量的所有炒版本都与$ ake $ $均等分布。我们的主要结果是代表双统计$（Cindex，Corners）$的生成函数，作为原始高斯多项式原始多项式的两变量Vandermonde卷积。证明依赖于不同华丽的路径之间的明确射击。
It is well known that Gaussian polynomials (i.e., $q$-binomials) describe the distribution of the $area$ statistic on monotone paths in a rectangular grid. We introduce two new statistics, $corners$ and $cindex$; attach ``ornaments'' to the grid; and re-evaluate these statistics, in order to argue that all scrambled versions of the $cindex$ statistic are equidistributed with $area$. Our main result is a representation of the generating function for the bi-statistic $(cindex,corners)$ as a two-variable Vandermonde convolution of the original Gaussian polynomial. The proof relies on explicit bijections between differently ornated paths.
