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.
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
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
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 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
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.
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.
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.
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.
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Partly supported by Foundation of Beijing Jiaotong University and by Beijing Natural Science Foundation(No.1012003)Partly supported by NSFC(No.10271017)Partly supported by NSFC(No.60373030)
