Simple formulas for constellations and bipartite maps with prescribed degrees

zbMath1436.05134MaRDI QIDQ2306511

Baptiste Louf

Publication date: 23 March 2020

Published in: Séminaire Lotharingien de Combinatoire (Search for Journal in Brave)

Full work available at URL: http://www.mat.univie.ac.at/~slc/wpapers/FPSAC2019//48.html

zbMATH Keywords

mapsHurwitz numbersconstellationsToda hierarchy

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) Enumerative problems (combinatorial problems) in algebraic geometry (14N10) Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) (14N35) Combinatorial aspects of algebraic geometry (05E14)

Related Items (3)

Planarity and non-separating cycles in uniform high genus quadrangulations ⋮ Combinatorics of Bousquet-Mélou-Schaeffer numbers in the light of topological recursion ⋮ Enumeration of non-oriented maps via integrability

Cites Work

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• Monotone Hurwitz numbers and the HCIZ integral
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• Toda equations for Hurwitz numbers
• The Toda equations and the Gromov-Witten theory of the Riemann sphere
• Fermionic approach to weighted Hurwitz numbers and topological recursion
• Planar maps as labeled mobiles
• Simple recurrence formulas to count maps on orientable surfaces
• Virasoro constraints and topological recursion for Grothendieck's dessin counting
• Asymptotic Enumeration of Constellations and Related Families of Maps on Orientable Surfaces
• A Census of Planar Maps
• A new family of bijections for planar maps
• Infinite wedge and random partitions

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