Explicit formulae for one-part double Hurwitz numbers with completed   3-cycles
  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. 
Viet Anh Nguyen
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