The Harer-Zagier and Jackson formulas and new results for one-face bipartite maps

Exact enumeration problems, generating functions (05A15) Combinatorial aspects of representation theory (05E10) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Relations of low-dimensional topology with graph theory (57M15)

Cites Work

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A simple model of trees for unicellular maps
Bijections and symmetries for the factorizations of the long cycle
Odd permutations are nicer than even ones
An analogue of the Harer-Zagier formula for unicellular maps on general surfaces
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Nombre de représentations d'une permutation comme produit de deux cycles de longueurs données
Hypermaps versus bipartite maps
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Graphs on surfaces and their applications. Appendix by Don B. Zagier
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Virasoro constraints and topological recursion for Grothendieck's dessin counting
Counting rooted maps by genus. I
A direct bijection for the Harer-Zagier formula
Another proof of the Harer-Zagier formula
A versatile combinatorial approach of studying products of long cycles in symmetric groups
Plane permutations and applications to a result of Zagier-Stanley and distances of permutations
Enumeration of Grothendieck's Dessins and KP Hierarchy
Counting Cycles in Permutations by Group Characters, With an Application to a Topological Problem
Rationality in map and hypermap enumeration by genus
Simple Formulas for Constellations and Bipartite Maps with Prescribed Degrees
Grothendieck’s dessins d’enfants in a web of dualities. III

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