Explicit formulae for one-part double Hurwitz numbers with completed 3-cycles

Viet Anh Nguyen (1)

1 LAREMA - Laboratoire Angevin de Recherche en Mathématiques

We prove two explicit formulae for one-part double Hurwitz numbers with completed 3-cycles. We define "combinatorial Hodge integrals" from these numbers in the spirit of the celebrated ELSV formula. The obtained results imply some explicit formulae and properties of the combinatorial Hodge integrals.

Mots clés: Hurwitz numbers; Hodge integrals; ELSV formula

Domaines: Mathématiques [math]

Viet Anh Nguyen. Explicit formulae for one-part double Hurwitz numbers with completed 3-cycles. 2016. ⟨hal-01280165⟩