Abstract:
Based on string duality Mari˜no and Vafa conjectured a closed formula on certain Hodge integrals in terms of representations of symmetric groups. This formula was first explicitly written down by the third author in and proved in joint work of the authors of the present paper. For a dierent approach see. Our proof follows the strategy of proving both sides of the equation satisfy the same cut-and-join equation and have the same initial values.

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