The asymptotic number of rooted maps on a surface
Journal of Combinatorial Theory Series A
The number of rooted maps on an orientable surface
Journal of Combinatorial Theory Series A
The number of degree restricted maps on general surfaces
Discrete Mathematics - Special issue on discrete mathematics in China
Systems of functional equations
Random Structures & Algorithms - Special issue: average-case analysis of algorithms
Regular Article: Enumeration of Planar Constellations
Advances in Applied Mathematics
Random maps, coalescing saddles, singularity analysis, and airy phenomena
Random Structures & Algorithms - Special issue on analysis of algorithms dedicated to Don Knuth on the occasion of his (100)8th birthday
Basic analytic combinatorics of directed lattice paths
Theoretical Computer Science
A bijection for covered maps, or a shortcut between Harer-Zagier's and Jackson's formulas
Journal of Combinatorial Theory Series A
Counting colored planar maps: Algebraicity results
Journal of Combinatorial Theory Series B
A simple model of trees for unicellular maps
Journal of Combinatorial Theory Series A
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We perform the asymptotic enumeration of two classes of rooted maps on orientable surfaces: m-hypermaps and m-constellations. For m = 2 they correspond respectively to maps with even face degrees and bipartite maps. We obtain explicit asymptotic formulas for the number of such maps with any finite set of allowed face degrees. Our proofs combine a bijective approach, generating series techniques related to lattice walks, and elementary algebraic graph theory. A special case of our results implies former conjectures of Z. Gao.