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.
KeywordsHurwitz numbers Symmetric groups Symmetric functions
This article is a part of my Ph.D. thesis that I am preparing under the supervision of Mattia Cafasso and Vladimir Roubtsov at LAREMA, UMR CNRS 6093. I am grateful to my supervisors for continuous support. I am also grateful to Bertrand Eynard and Vincent Rivasseau for having guided my first steps in research with extreme care during my research internship. This experience played a key role in my decision to continue the hard path of research. My Ph.D. study is funded by the French ministerial scholarship “Allocations Spécifiques Polytechniciens”. My research is also partially supported by LAREMA and the Nouvelle Équipe “Topologie algébrique et Physique Mathématique” of the Pays de la Loire region.