This paper provides the number of combinatorially distinct general rooted Eulerian planar maps with the number of edges and the valency of rooted vertex of the maps as. two parameters. It is also an answer to open pro...This paper provides the number of combinatorially distinct general rooted Eulerian planar maps with the number of edges and the valency of rooted vertex of the maps as. two parameters. It is also an answer to open problem 7.1 in [1]. Meanwhile, the case of three variables can be derived by using Lagrangian inversion.展开更多
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
This paper provides a functional equation satisfied by the dichromatic sum function of rooted outer-planar maps. By the equation, the dichromatic sum function can be found explicitly.
A map is bisingular if each edge is either a loop (This paper only considers planar loop) or an isthmus (i.e., on the boundary of the same face). This paper studies the number of rooted bisingular maps on the sphere a...A map is bisingular if each edge is either a loop (This paper only considers planar loop) or an isthmus (i.e., on the boundary of the same face). This paper studies the number of rooted bisingular maps on the sphere and the torus, and also presents formulae for such maps with three parameters: the root-valency, the number of isthmus, and the number of planar loops.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.
It is well known that singular maps(i.e.,those have only one face on a surface)play a key role in the theory of up-embeddability of graphs.In this paper the number of rooted singular maps on the Klein bottle is studie...It is well known that singular maps(i.e.,those have only one face on a surface)play a key role in the theory of up-embeddability of graphs.In this paper the number of rooted singular maps on the Klein bottle is studied.An explicit form of the enumerating function according to the root-valency and the size of the map is determined.Further,an expression of the vertex partition function is also found.展开更多
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 we provide a solution of the functional equation unsolved in the paper, by the second author, "On functional equations arising from map enumerations" that appeared in Discrete Math, 123: 93-109...In this paper we provide a solution of the functional equation unsolved in the paper, by the second author, "On functional equations arising from map enumerations" that appeared in Discrete Math, 123: 93-109 (1993). It is also the number of combinatorial distinct rooted general eulerian planar maps with the valency of root-vertex, the number of non-root vertices and non-root faces of the maps as three parameters. In particular, a result in the paper, by the same author, "On the number of eulerian planar maps" that appeared in Acta Math Sinica, 12: 418-423 (1992) is simplified.展开更多
This paper provides some functional equations satisfied by the generatingfunctions for enumerating general rooted planar maps with up to three parameters. Furthermore, thegenerating functions can be obtained explicitl...This paper provides some functional equations satisfied by the generatingfunctions for enumerating general rooted planar maps with up to three parameters. Furthermore, thegenerating functions can be obtained explicitly by employing the Lagrangian inversion. This is alsoan answer to an open problem in 1989.展开更多
In this paper a special kind of triangulated maps on the sphere called fair triangulations is enumerated with the size of maps as parameter.Moreover,the number of several other kinds of triangulations are enumerated a...In this paper a special kind of triangulated maps on the sphere called fair triangulations is enumerated with the size of maps as parameter.Moreover,the number of several other kinds of triangulations are enumerated as well.展开更多
A map is 4-regular unicursal if all its vertices are 4-valent except two odd-valent vertices. This paper investigates the number of rooted 4-regular unicursal planar maps and presents some formulae for such maps with ...A map is 4-regular unicursal if all its vertices are 4-valent except two odd-valent vertices. This paper investigates the number of rooted 4-regular unicursal planar maps and presents some formulae for such maps with four parameters： the number of edges, the number of inner faces and the valencies of the two odd vertices.展开更多
This paper investigates the number of rooted unicursal planar maps and presents some formulae for such maps with four parameters： the numbers of nonrooted vertices and inner faces and the valencies of two odd vertices.
This paper provides the parametric expressions satisfied by the enumerating functions for rooted nearly cubic c-nets with the size and/or the root-vertex valency of the maps as the parameters via nonseparable nearly ...This paper provides the parametric expressions satisfied by the enumerating functions for rooted nearly cubic c-nets with the size and/or the root-vertex valency of the maps as the parameters via nonseparable nearly cubic maps. On this basis, two explicit expressions of the functions can be derived by employing Lagrangian inversion.展开更多
文摘This paper provides the number of combinatorially distinct general rooted Eulerian planar maps with the number of edges and the valency of rooted vertex of the maps as. two parameters. It is also an answer to open problem 7.1 in [1]. Meanwhile, the case of three variables can be derived by using Lagrangian inversion.
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.
基金Supported by the National Natural Science Foundation of China
文摘This paper provides a functional equation satisfied by the dichromatic sum function of rooted outer-planar maps. By the equation, the dichromatic sum function can be found explicitly.
基金Supported by fifteenth programming of Central University for Nationalities, NNSFC under Grant No.10271048 and 19831080
文摘A map is bisingular if each edge is either a loop (This paper only considers planar loop) or an isthmus (i.e., on the boundary of the same face). This paper studies the number of rooted bisingular maps on the sphere and the torus, and also presents formulae for such maps with three parameters: the root-valency, the number of isthmus, and the number of planar loops.
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the National Natural Science Foundation of China(1 983 1 0 80 )
文摘It is well known that singular maps(i.e.,those have only one face on a surface)play a key role in the theory of up-embeddability of graphs.In this paper the number of rooted singular maps on the Klein bottle is studied.An explicit form of the enumerating function according to the root-valency and the size of the map is determined.Further,an expression of the vertex partition function is also found.
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.
基金the National Natural Science Foundation of China (Grant No. 10271017)
文摘In this paper we provide a solution of the functional equation unsolved in the paper, by the second author, "On functional equations arising from map enumerations" that appeared in Discrete Math, 123: 93-109 (1993). It is also the number of combinatorial distinct rooted general eulerian planar maps with the valency of root-vertex, the number of non-root vertices and non-root faces of the maps as three parameters. In particular, a result in the paper, by the same author, "On the number of eulerian planar maps" that appeared in Acta Math Sinica, 12: 418-423 (1992) is simplified.
基金Project 10271017 supported by National Natural Science Foundation of China
文摘This paper provides some functional equations satisfied by the generatingfunctions for enumerating general rooted planar maps with up to three parameters. Furthermore, thegenerating functions can be obtained explicitly by employing the Lagrangian inversion. This is alsoan answer to an open problem in 1989.
基金This article is supported by National Natural Science Foundation of China (19701002)
文摘In this paper a special kind of triangulated maps on the sphere called fair triangulations is enumerated with the size of maps as parameter.Moreover,the number of several other kinds of triangulations are enumerated as well.
基金Supported by the National Natural Science Foundation of China(No.10271017,11371133,11571044)the Natural Science Foundation Project of Chongqing(No.cstc2012jj A00041,cstc2014jcyj A00041)the Innovation Foundation of Chongqing(No.KJTD201321)
文摘A map is 4-regular unicursal if all its vertices are 4-valent except two odd-valent vertices. This paper investigates the number of rooted 4-regular unicursal planar maps and presents some formulae for such maps with four parameters： the number of edges, the number of inner faces and the valencies of the two odd vertices.
基金Supported by the National Natural Science Foundation of China(No.10271017)the Natural Science Foundation Project of Chongqing(N0.cstc2012jjA00041)Chongqing Innovation Fund(grant no.KJTD201321)
文摘This paper investigates the number of rooted unicursal planar maps and presents some formulae for such maps with four parameters： the numbers of nonrooted vertices and inner faces and the valencies of two odd vertices.
基金This Research is supported by National Natural Science Foundation of China (No. 19831080).
文摘This paper provides the parametric expressions satisfied by the enumerating functions for rooted nearly cubic c-nets with the size and/or the root-vertex valency of the maps as the parameters via nonseparable nearly cubic maps. On this basis, two explicit expressions of the functions can be derived by employing Lagrangian inversion.
