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      A new formula for intersection numbers

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          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.

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          Author and article information

          Journal
          08 December 2022
          Article
          2212.04256
          a8972848-af00-4f64-92cd-206a586438d4

          http://creativecommons.org/licenses/by/4.0/

          Custom metadata
          14C17, 37K10, 14H70
          45 pages, 10 pages of appendix
          math-ph math.AG math.CO math.MP

          Mathematical physics,Combinatorics,Mathematical & Computational physics,Geometry & Topology

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