A new formula for intersection numbers
Abstract
We propose a new formula to compute WittenKontsevich 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 semistandard 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.
 Publication:

arXiv eprints
 Pub Date:
 December 2022
 DOI:
 10.48550/arXiv.2212.04256
 arXiv:
 arXiv:2212.04256
 Bibcode:
 2022arXiv221204256E
 Keywords:

 Mathematical Physics;
 Mathematics  Algebraic Geometry;
 Mathematics  Combinatorics;
 14C17;
 37K10;
 14H70
 EPrint:
 43 pages, 9 pages of bibliography/appendices, misprints corrected, notation simplified, results unchanged