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BISINGULAR MAPS ON SOME SURFACES 认领 引用
1
作者 李赵祥 任韩 刘彦佩 《Acta Mathematica Scientia》 SCIE 2004年第2期313-320,共8页
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
关键词 Bisingular map enumerating function Lagrangian inversion
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SINGULAR MAPS ON THE KLEIN BOTTLE 认领 引用
2
作者 Li Zhaoxiang Liu YanpeiDept.of Math.,Northern Jiaotong Univ.,Beijing 100044,China. 《Applied Mathematics(A Journal of Chinese Universities)》 2002年第3期365-370,共6页
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
关键词 singular map enumerating function Lagrangian inversion.
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A Census of Petal Bundles by Genus 认领 引用 被引量：1
3
作者 Yan XU Yan Pei LIU 《Acta Mathematica Sinica,English Series》 SCIE 2008年第6期937-946,共10页
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
关键词 rooted map enumerating function enumeration petal bundles
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The Number of Nonseparable Maps on the Projective Plane 认领 引用
4
作者 Zhao-xiang Li Li-ying Mou +1 位作者 Fen Lei Jie Xu 《Acta Mathematicae Applicatae Sinica》 SCIE 2010年第3期489-494,共6页
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 ... 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
关键词 Nonseparable maps Enumerating function Asymptotic evaluation
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Chromatic Sums of Biloopless Nonseparable Near-Triangulations on the Projective Plane 认领 引用
5
作者 Zhao-xiang Li Yan-pei Liu Bing-feng Si 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2013年第1期123-134,共12页
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
关键词 chromatic sum function biloopless triangulation enumerating function
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Chromatic Sums of Nonseparable Near-Triangulations on the Projective Plane 认领 引用
6
作者 Zhao Xiang LI Wei HE 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2012年第11期2185-2196,共12页
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
关键词 Triangulation chromatic sum function enumerating function asymptotic evaluation
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Counting Rooted Unicursal Planar Maps 认领 引用
7
作者 Shu-de LONG Jun-liang CAI 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2013年第4期749-764,共16页
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.
关键词 unicursal planar map enumerating function functional equation Lagrangian inversion
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Counting Rooted 4-regular Unicursal Planar Maps 认领 引用
8
作者 Shu-de LONG Jun-liang CAI 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2017年第4期909-918,共10页
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
关键词 unicursal planar map enumerating function functional equation Lagrangian inversion
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The Number of Rooted Circuit Boundary Maps 认领 引用
9
作者 Yan XU Yan Pei LIU 《Acta Mathematica Sinica,English Series》 SCIE 2010年第9期1653-1666,共14页
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
关键词 Rooted map enumerating function enumeration circuit boundary maps
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