From this point of view, our result generalizes a formula of Walsh and Lehman [19, Formula 9] for some monochromatic maps to the corresponding bicolored maps.

We present an explicit expression for the number of decompositions of ann-cycle as a product of any two permutations of cycle types given by partitions λ and μ.

We present an explicit expression for the number of decompositions of ann-cycle as a product of any two permutations of cycle types given by partitions and .

Abstract. We show that, for any fixed genus g, the ordinary generating function for the genus g partitions of an n-element set into k blocks is algebraic.

Jun 19, 2013 · Schaeffer, Factoring N-cycles and Counting Maps of Given Genus, European J. Combin. 19 (1998), 819–834. [7] G. Hetyei, Central Delannoy ...

Feb 15, 2024 · Abstract. We study the enumeration of set partitions, according to their length, number of parts, cyclic type, and genus.

Goupil and G. Schaeffer, Factoring N-cycles and Counting Maps of Given Genus, European J. Combin. 19 (1998), 819–834.

May 1, 2023 · We study the enumeration of set partitions, according to their length, number of parts, cyclic type, and genus. We introduce genus-dependent ...

May 17, 2013 · Our work is devoted to the bijective enumeration of the set of factorizations of a permutation into m factors with a given number of cycles.

Oct 7, 2024 · We are now interested in enumerating all one-face bipartite maps (ω,σ,π) of n edges and genus g where the cycle-type of the hyperedge σ is γ = ( ...