Rationality in map and hypermap enumeration by genus

DOI10.1090/spmj/1501zbMath1385.05040arXiv1609.05493OpenAlexW2963817836MaRDI QIDQ4636963

Peter Zograf, Maxim E. Kazaryan

Publication date: 17 April 2018

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.05493

zbMATH Keywords

ribbon graphsGrothendieck's dessins d'enfantsenumeration of mapsenumeration of hypermaps

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Enumeration in graph theory (05C30)

Related Items (2)

Quantization of Harer-Zagier formulas ⋮ Quasi-polynomiality of monotone orbifold Hurwitz numbers and Grothendieck's dessins d'enfants

Cites Work

• Enumeration of unrooted hypermaps of a given genus
• An analog of the Harer-Zagier formula for unicellular bicolored maps
• Hypermaps versus bipartite maps
• The Euler characteristic of the moduli space of curves
• Simple recurrence formulas to count maps on orientable surfaces
• Virasoro constraints and topological recursion for Grothendieck's dessin counting
• Enumeration of unrooted maps of a given genus
• Counting rooted maps by genus. I
• Combinatorial solutions to integrable hierarchies
• Enumeration of Grothendieck's Dessins and KP Hierarchy
• Counting Cycles in Permutations by Group Characters, With an Application to a Topological Problem
• Enumeration of hypermaps of a given genus
• A Census of Planar Maps

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