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BISINGULAR MAPS ON SOME SURFACES

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Acta Mathematica Scientia 2004年第2期24卷 313-320页

作者：李赵祥任韩刘彦佩 DepartmentofMathematics CentralUniversityforNationalitiesBeijing100081China

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.

关键词： Bisingular map enumerating function lagrangian inversion

Counting Rooted 4-regular Unicursal Planar Maps

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Acta Mathematicae Applicatae Sinica 2017年第4期33卷 909-918页

作者： Shu-de LONG Jun-liang CAI Department of Mathematics Chongqing University of Arts and Sciences School of Mathematical Sciences Beijing Normal University

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 ... 详细信息

关键词： unicursal planar map enumerating function functional equation lagrangian inversion

COUNTING FAIR NEAR-TRIANGULATIONS ON THE DISC

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Acta Mathematica Scientia 2000年第1期20卷 49-54页

作者：任韩刘颜佩 Department of Mathematics Suzhou University Suzhou 215006 China Department of Mathematics Northern Jiaotong University Beijing 100044 China

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.

关键词： map,fair near-triangulation enufunction lagrangian inversion

The Enumeration of General Rooted Planar Maps

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Acta Mathematica Sinica,English Series 2005年第1期21卷 215-224页

作者： JunLiangCAI YahPeiLIU DepartmentofMathematics Beijin9NormalUniversityBeijin9100875P.R.China DepartmentofMathematics NorthernJiaotongUniversityBeijing100044P.R.China

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... 详细信息

关键词： Planar map Functional equation Parametric expression lagrangian inversion

On the Number of Fair Triangulations

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Acta Mathematica Sinica,English Series 2000年第1期16卷 79-84页

作者： Han Ren Department of Mathematics,Xiamen University,Xiamen 361005,P.R.ChinaYanpei Liu Department of Mathematics,Northern JiaoTong University,Beijin 100044,P.R.China Department of Mathematics Xiamen University Xiamen 361005 P.R. China Department of Mathematics Northern JiaoTong University Beijin 100044 P.R. China

In this paper a special kind of triangulated maps on the sphere called fair triangulations is enumerated with the size of maps as ***,the number of several other kinds of triangulations are enumerated as well.

关键词： Map Triangulation Enumeration lagrangian inversion

ENUMERATING ROOTED EULERIAN PLANAR MAPS

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Acta Mathematica Scientia 2001年第3期21卷 289-294页

作者：蔡俊亮郝荣霞刘彦佩 Department of Mathematics Beijing Normal University Beijing 100875 China Department of Mathematics Northern Jiaotong University Beijing 100044 China

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... 详细信息

关键词： Eulerian map functional equation lagrangian inversion

THE NUMBER OF ROOTED NEARLY CUBIC C-NETS

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Acta Mathematicae Applicatae Sinica 2001年第1期17卷 29-37页

作者：蔡俊亮刘彦佩 Department of Mathematics Beijing Normal University Beijing China Department of Mathematics Northern Jiaotong University Beijing China

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.

关键词： Planar map enumerating equation generating function lagrangian inversion

Counting Non-separable Near-triangulations on the Mobius Band

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Communications in Mathematical Research 1999年第1期 115-120页

作者： Ren Han Liu Yanpei and Liu Tongyin (Department of Mathematics, Northern Jiaotong University, Beijing, 100044)

§１．ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｅｎｕｍｅｒａｔｉｏｎｏｆｒｏｏｔｅｄｐｌａｎａｒｍａｐｓｗａｓｎｏｔｉｃｅｄｆｉｒｓｔｂｙＴｕｔｅｉｎ１９６３，ａｎｄｉｎｈｉｓｆｉｒｓｔｐａｐｅｒｉｎｔｈｉｓａｒｅａｈｅｐｒｏ... 详细信息

§１．ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｅｎｕｍｅｒａｔｉｏｎｏｆｒｏｏｔｅｄｐｌａｎａｒｍａｐｓｗａｓｎｏｔｉｃｅｄｆｉｒｓｔｂｙＴｕｔｅｉｎ１９６３，ａｎｄｉｎｈｉｓｆｉｒｓｔｐａｐｅｒｉｎｔｈｉｓａｒｅａｈｅｐｒｏｖｉｄｅｄａｎｅｎｕｆｕｎｃｔｉｏ...

关键词： Rooted Map lagrangian inversion Enufunction