Combinatorics of binomial decompositions of the simplest Hodge integrals

Abstract

We reduce the calculation of the simplest Hodge integrals to some sums over decorated trees. Since Hodge integrals are already calculated, this gives a proof of a rather interesting combinatorial theorem and a new representation of Bernoulli numbers.

16 pages

References in corpus (4)

• Hurwitz numbers and intersections on moduli spaces of curves
• Geometry of meromorphic functions and intersections on moduli spaces of curves
• Hodge integrals and Hurwitz numbers via virtual localization
• Topological recursive relations in $H^{2g}(M_{g,n})$

Cited by in corpus (3)

• A new proof of Faber's intersection number conjecture
• Buryak-Okounkov formula for the $n$-point function and a new proof of the Witten conjecture
• Faber's socle intersection numbers via Gromov--Witten theory of elliptic curve