论文标题
交叉数字的新公式
A new formula for intersection numbers
论文作者
论文摘要
我们提出了一个新的公式来计算Witten-Kontsevich交叉数字。它是一个封闭的公式，不涉及递归既不求解方程式。它仅涉及阶乘产品的分区，双阶乘数量和Kostka数字（具有给定形状和重量的半标准图表的数量）的总和。作为一种应用，我们证明了[ELO21]的猜想，表明以基本对称多项式表示的相交数的生成多项式具有意外消失的系数。
We propose a new formula to compute Witten--Kontsevich intersection numbers. It is a closed formula, not involving recursion neither solving equations. It only involves sums over partitions of products of factorials, double factorials and Kostka numbers (numbers of semi-standard tableau of given shape and weight) with bounded weights. As an application, we prove a conjecture of [ELO21] stating that the generating polynomials of the intersection numbers expressed in the basis of elementary symmetric polynomials have an unexpected vanishing of their coefficients.
