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
MUKAIDONO proposed and systematically investigated the theory of regular ternary logic functions that meets the need of uncertain inferences. The enumeration of ternary logic functions is very complicated and several ...MUKAIDONO proposed and systematically investigated the theory of regular ternary logic functions that meets the need of uncertain inferences. The enumeration of ternary logic functions is very complicated and several results have been obtained only in the case where the number of variables is less than 7. In this letter we offer a new possible way to solve the prob-展开更多
This paper provides the uniform enumerative functional equation of orientable （nonori-entable） rooted petal bundles with more parameters, and deduces two recursion formulas for calculation. Accordingly, an explicit ...This paper provides the uniform enumerative functional equation of orientable （nonori-entable） rooted petal bundles with more parameters, and deduces two recursion formulas for calculation. Accordingly, an explicit expression of rooted petal bundles with up to two parameters on nonorientable surface of genus 4 is also obtained.展开更多
In this article, the authors discuss two kinds of new planar maps： pan-fan maps and circuit boundary maps, and provide explicit expressions about their enumerating functions with different parameters. Meanwhile, two ...In this article, the authors discuss two kinds of new planar maps： pan-fan maps and circuit boundary maps, and provide explicit expressions about their enumerating functions with different parameters. Meanwhile, two explicit counting formulas for circuit cubic boundary maps with two parameters; the size and the valency of the root-face, are also extracted.展开更多
In this paper, the chromatic sum functions of rooted biloopless nonsepavable near-triangulations on the sphere and the projective plane are studied. The chromatic sum function equations of such maps are obtained. From...In this paper, the chromatic sum functions of rooted biloopless nonsepavable near-triangulations on the sphere and the projective plane are studied. The chromatic sum function equations of such maps are obtained. From the chromatic sum equations of such maps, the enumerating function equations of such maps are derived. An asymptotic evaluation and some explicit expression of enumerating functions are also derived.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.
In this paper, we study the chromatic triangulations on the sphere and the projective plane. sum functions of rooted nonseparable near- The chromatic sum function equations of such maps are obtained. From the chromati...In this paper, we study the chromatic triangulations on the sphere and the projective plane. sum functions of rooted nonseparable near- The chromatic sum function equations of such maps are obtained. From the chromatic sum equations of such maps, the enumerating function equa- tions of such maps are derived. Applying chromatic sum theory, the enumerating problem of different sorts maps can be studied, and a new method of enumeration can be obtained. Moreover, an asymptotic evaluation and some explicit expression of enumerating functions are also derived.展开更多
In this paper, we study the rooted nonseparable maps on the sphere and the projective plane with the valency of root-face and the number of edges as parameters. Explicit expression of enumerating functions are obtaine...In this paper, we study the rooted nonseparable maps on the sphere and the projective plane with the valency of root-face and the number of edges as parameters. Explicit expression of enumerating functions are obtained for such maps on the sphere and the projective plane. A parametric expression of the generating function is obtained for such maps on the projective plane, from which asymptotic evaluations are derived. Moreover, if the number of edges is sufficiently large, then almost all nonseparable maps on the projective plane are not triangulation.展开更多
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.
文摘MUKAIDONO proposed and systematically investigated the theory of regular ternary logic functions that meets the need of uncertain inferences. The enumeration of ternary logic functions is very complicated and several results have been obtained only in the case where the number of variables is less than 7. In this letter we offer a new possible way to solve the prob-
基金NNSFC under Grant No.60373030 and Grant No.10571031
文摘This paper provides the uniform enumerative functional equation of orientable （nonori-entable） rooted petal bundles with more parameters, and deduces two recursion formulas for calculation. Accordingly, an explicit expression of rooted petal bundles with up to two parameters on nonorientable surface of genus 4 is also obtained.
文摘In this article, the authors discuss two kinds of new planar maps： pan-fan maps and circuit boundary maps, and provide explicit expressions about their enumerating functions with different parameters. Meanwhile, two explicit counting formulas for circuit cubic boundary maps with two parameters; the size and the valency of the root-face, are also extracted.
基金Supported by the National Natural Science Foundation of China (No. 10771225 10871021+1 种基金 71071016) Fundamental Research Funds for the Central Universities
文摘In this paper, the chromatic sum functions of rooted biloopless nonsepavable near-triangulations on the sphere and the projective plane are studied. The chromatic sum function equations of such maps are obtained. From the chromatic sum equations of such maps, the enumerating function equations of such maps are derived. An asymptotic evaluation and some explicit expression of enumerating functions are also derived.
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Supported by National Natural Science Foundation of China (Grant No. 10771225)
文摘In this paper, we study the chromatic triangulations on the sphere and the projective plane. sum functions of rooted nonseparable near- The chromatic sum function equations of such maps are obtained. From the chromatic sum equations of such maps, the enumerating function equa- tions of such maps are derived. Applying chromatic sum theory, the enumerating problem of different sorts maps can be studied, and a new method of enumeration can be obtained. Moreover, an asymptotic evaluation and some explicit expression of enumerating functions are also derived.
基金Supported by the National Natural Science Foundation of China (No. 10771225)the project of science research plan of The State Ethnic Affairs Commission of PRC (No. 07ZY04)the project of "211" of Minzu University of China (No. 021211030312)
文摘In this paper, we study the rooted nonseparable maps on the sphere and the projective plane with the valency of root-face and the number of edges as parameters. Explicit expression of enumerating functions are obtained for such maps on the sphere and the projective plane. A parametric expression of the generating function is obtained for such maps on the projective plane, from which asymptotic evaluations are derived. Moreover, if the number of edges is sufficiently large, then almost all nonseparable maps on the projective plane are not triangulation.
