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.
- Pub Date:
- December 2022
- Mathematical Physics;
- Mathematics - Algebraic Geometry;
- Mathematics - Combinatorics;
- 43 pages, 9 pages of bibliography/appendices, misprints corrected, notation simplified, results unchanged