A generalization of the language of Łukasiewicz coding rooted planar hypermaps
Theoretical Computer Science - Random generation of combinatorial objects and bijective combinatorics
Submap Density and Asymmetry Results for Two Parameter Map Families
Combinatorics, Probability and Computing
Polynomial equations with one catalytic variable, algebraic series and map enumeration
Journal of Combinatorial Theory Series B
Counting colored planar maps: Algebraicity results
Journal of Combinatorial Theory Series B
Unified bijections for maps with prescribed degrees and girth
Journal of Combinatorial Theory Series A
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Let $D$ be a set of positive integers. Let $m(n)$ be the number of $n$ edged rooted maps on the sphere, all of whose vertex degrees (or, dually, face degrees) lie in $D$. Using Brown's technique, the generating function for $m(n)$ implicitly is obtained. It is used to prove that, when gcd ($D$) is even, $$ m(n)\equiv C(D)n^{5/2}\lambda(D)^n. $$ It also yields known formulas for various special $D$.