A new formula for intersection numbers
Mathematical Physics
2023-02-20 v2 Algebraic Geometry
Combinatorics
math.MP
Abstract
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.
Cite
@article{arxiv.2212.04256,
title = {A new formula for intersection numbers},
author = {Bertrand Eynard and Dimitrios Mitsios},
journal= {arXiv preprint arXiv:2212.04256},
year = {2023}
}
Comments
43 pages, 9 pages of bibliography/appendices, misprints corrected, notation simplified, results unchanged