The functional equation satisfied by the vertex partition function of rooted loopless Eulerianplanar maps is provided. As applications, the enumerating equations for general and regular casesof this kind of maps are a...The functional equation satisfied by the vertex partition function of rooted loopless Eulerianplanar maps is provided. As applications, the enumerating equations for general and regular casesof this kind of maps are also discussed.展开更多
Terminologies not explained here refer to [1] on enumeration, to [2, 3] on functional equations, and to [4] on combinatorial maps. Let (?) be a set of all rooted planar maps. For N∈(?); let m(N) and n_i(N), i≥1 repr...Terminologies not explained here refer to [1] on enumeration, to [2, 3] on functional equations, and to [4] on combinatorial maps. Let (?) be a set of all rooted planar maps. For N∈(?); let m(N) and n_i(N), i≥1 represent the valency of the root-vertex and the number of non-root-vertices with valency i in N. All maps considered here are rooted loopless Eulerian planar maps. Let ? be a set of展开更多
基金This project is supported partially by the National Natural Science Foundation of China Grant 18971061
文摘The functional equation satisfied by the vertex partition function of rooted loopless Eulerianplanar maps is provided. As applications, the enumerating equations for general and regular casesof this kind of maps are also discussed.
基金Project supported by the National Natural Science Foundation of China
文摘Terminologies not explained here refer to [1] on enumeration, to [2, 3] on functional equations, and to [4] on combinatorial maps. Let (?) be a set of all rooted planar maps. For N∈(?); let m(N) and n_i(N), i≥1 represent the valency of the root-vertex and the number of non-root-vertices with valency i in N. All maps considered here are rooted loopless Eulerian planar maps. Let ? be a set of
基金Supported by NSFC(No.10271017,No.11371133)Natural Science Foundation Project of Chongqing(No.cstc2012jjA00041)Chongqing Innovation Fund(No.KJTD201321)
