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# Communications in Number Theory and Physics

## Volume 4 (2010)

### Number 2

### Polynomial recursion formula for linear Hodge integrals

Pages: 267 – 293

DOI: http://dx.doi.org/10.4310/CNTP.2010.v4.n2.a1

#### Authors

#### Abstract

We establish a polynomial recursion formula forlinear Hodge integrals. It is obtained as the Laplacetransform of the cut-and-join equation for the simpleHurwitz numbers. We show that the recursion recovers the Witten–Kontsevichtheorem when restricted to the top degree terms, andalso the combinatorial factor of the$\lam_g$ formula as the lowest degree terms.