Hodge integrals, Hurwitz numbers, and Symmetric Groups

Details Hodge integrals, Hurwitz numbers, and Symmetric Groups Hodge integrals, Hurwitz numbers, and Symmetric Groups

2003-08-04

arxiv.org/abs/math/0308024v1

Mathematics

Algebraic Geometry

24 pages

Scientific paper

We prove some combinatorial results related to a formula on Hodge integrals conjectured by Mari\~no and Vafa. These results play important roles in the proof and applications of this formula by the author jointly with Chiu-Chu Melissa Liu and Kefeng Liu. We also compare with some related results on Hurwitz numbers and obtain some closed expressions for the generating series of Hurwitz numbers and the related Hodge integrals.

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