In this article the rooted planar near-4-regular Eulerian trails are enum erated and an explicit form ula for such m aps is presented. Further, the rooted near-4-regular Eulerian m aps on the torus are counted in an...In this article the rooted planar near-4-regular Eulerian trails are enum erated and an explicit form ula for such m aps is presented. Further, the rooted near-4-regular Eulerian m aps on the torus are counted in an exact w ay.展开更多
It is well known that any kind of exact enumerations of rooted maps on nonplanar surface is quite difficult. This paper presents a functional equation for rooted Eulerian maps on the projective plane. A parametric exp...It is well known that any kind of exact enumerations of rooted maps on nonplanar surface is quite difficult. This paper presents a functional equation for rooted Eulerian maps on the projective plane. A parametric expression, through which an exact enumeration by root-valency and the number of edges of maps may be determined, is obtained.展开更多
In this paper various kinds of fair near-triangulations are enumerated and several other types of near-triangulations are counted with the root-face valency, the number of edges and faces as the parameters.
In this article we count the number of rooted planar Eulerian trails and present an explicit enufunction for such maps. Based on this result, we count rooted Eulerian maps on the torus in an exact way.
In this paper we present a parametric expression on the enumeration of rooted non-separable near-triangulations on the cylinder which is much related to the maps on the torus.
In this paper, general functional equations of rooted essential maps on surfaces （orientable and nonorientable） are deduced and their formal solutions are presented. Further, three explicit for- mulae for counting e...In this paper, general functional equations of rooted essential maps on surfaces （orientable and nonorientable） are deduced and their formal solutions are presented. Further, three explicit for- mulae for counting essential maps on S2,N3 andN4 are given. In the same time, some known results can be derived.展开更多
文摘In this article the rooted planar near-4-regular Eulerian trails are enum erated and an explicit form ula for such m aps is presented. Further, the rooted near-4-regular Eulerian m aps on the torus are counted in an exact w ay.
文摘It is well known that any kind of exact enumerations of rooted maps on nonplanar surface is quite difficult. This paper presents a functional equation for rooted Eulerian maps on the projective plane. A parametric expression, through which an exact enumeration by root-valency and the number of edges of maps may be determined, is obtained.
文摘In this paper various kinds of fair near-triangulations are enumerated and several other types of near-triangulations are counted with the root-face valency, the number of edges and faces as the parameters.
基金Project supported by the Shanghai City Foundation of Selected Academic Research.
文摘In this article we count the number of rooted planar Eulerian trails and present an explicit enufunction for such maps. Based on this result, we count rooted Eulerian maps on the torus in an exact way.
基金Supported by the Natural Science Foundation of China !(19701002)
文摘In this paper we present a parametric expression on the enumeration of rooted non-separable near-triangulations on the cylinder which is much related to the maps on the torus.
文摘In this paper, general functional equations of rooted essential maps on surfaces （orientable and nonorientable） are deduced and their formal solutions are presented. Further, three explicit for- mulae for counting essential maps on S2,N3 andN4 are given. In the same time, some known results can be derived.
