带根2-连通3-正则平面地图计数

本文利用不可分离的3-正则有根平面地图的计数结果,间接地给出了2-连通 3-正则有根平面地图依边数和根面次的计数显式．     

带根4-正则单行平面地图的计数(英文)

本文研究了带根4-正则单行平面地图的计数问题,并给出了以其非根点数和两个奇点次为三个参数的一些计数公式.     

球面和射影平面上不可分地图的色和

给出了球面和射影平面上带根不可分地图的色和方程,从色和方程导出了球面和射影平面上带根一般不可分地图、二部地图的计数函数方程. 利用色和理论,研究不同类地图的计数问题,得到了一种研究计数问题的新方法. 此外,还得到了一些计数显示表达式.     

射影平面上的对偶无环不可分近三角剖分地图

本文研究了球面和射影平面上对偶无环不可分近三角剖分带根地图的以根面次和内面数为参数的计数问题,得到了这类地图在球面和射影平面上的计数函数满足的方程.还得到了射影平面上2连通地图一个参数的显示表达式和渐近估计式.     

带根无环欧拉平面地图的计数(英文)

自20世纪60年代初Tutte的开创性工作以来,许多学者在带根地图的计数方面作了很多工作,但许多类无环地图的计数仍没有被处理.本文主要研究以根点次、非根点数和内面数为三个参数的带根无环欧拉平面地图的计数问题.     

曲面上构造三次3-连通非Hamiltonian地图的一种方法(英文)

Tutte在1946年构造性证明了并非每个简单的3-凸胞腔都是Hamiltonian的后,人们又陆续提出了多种构造三次3-连通非Hamiltonian平面图的方法,但无一能用于在一般曲面上寻找三次3-连通非Hamiltonian地图.本文提出了一种新的构造方法,可在任一个曲面上构造出三次3-连通非Hamiltonian地图.     

曲面上构造三次3—连通非Hamiltonian地图的一种方法

Tutte在1946年构造性证明了并非每个简单的3-凸胞腔都是Hamiltonian的后，人们又陆续提出了多种构造三次3-连通非Hamiltonian平面图的方法，但无一能用于在一般曲面上寻找三次3-连通非Hamiltonian地图，本文提出了一种新的构造方法，可在任一曲面上构造出三次3-连通非Hamiltonian地图。     

有根无环平面地图节点剖分计数方程

一个平面地图,如果无有边是环,则称为是无环的.有根的意义与[1]中的相同.在那里对于此类地图的一些计数问题作了研究,但从未触及到节点剖分.这篇文章的主要目的在于研究这类地图的依节点剖分的计数.求出了有根无环平面地图依节点剖分计数的母函数所满足的一个泛函方程.并且,作为这一方程的一种应用,求出了一类在节点的最大次给定情况下的有根无环平面地图依节点剖分计数的一些结果.     

近三正则3—连通平面地图的计数

本文提供了便于依根点次,边数和根面次计数近三正则3－连通有根平面地图的一个函数方程,继之得到其参数形式解,并由此通过Lagrange反演导出了它的计数显示,本文推广了[3]和[4]的结果。     

Klein瓶上的双奇异地图

一个地图的每条边如果不是环就是割边(即该边的两边是同一个面的边界)，则称之为双奇异地图，本文研究Klein瓶上带根双奇异地图的计数问题，得到了此类地图以边数、平面环数、手柄上本质环数和又帽上本质环数为参数的计数公式，并得到了部分计数显式。     

THE NUMBER OF ROOTED NEARLY CUBIC C-NETS

1. IntroductionW.T. Tutte's original papers[1--3) on the enumerative theory of rooted planar maps havebrought forth a series of papers on enumerating triangulations. The enumeration of generalrooted planar maps has then also been investigated and a number of elegant results havebeen obtained, although relatively fewer than that of triangulations. As the dual case oftriangulations, the enumerative theory of cubic maps has also been developed, though thereare a lot of problems waiting for solut…     

The enumeration of rooted cubic c-nets

This paper is to establish a functional equation satisfied by the generating function for counting rooted cubic c-nets and then to determine the parametric expressions of the equation directly. Meanwhile, the explicit formulae for counting rooted cubic c-nets are derived immediately by employing Lagrangian inversion with one or two parameters. Both of them are summation-free and in which one is just an answer to the open problem (8.6.5) in [1].     

A census of boundary cubic rooted planar maps

In this paper, boundary cubic rooted planar maps are investigated and exact enumerative formulae are given. First, an enumerative formula for boundary cubic inner-forest maps with the size (number of edges) as a parameter is derived. For the special case of boundary cubic inner-tree maps, a simple formula with two parameters is presented. Further, according to the duality, a corresponding result for outer-planar maps is obtained. Finally, some results for boundary cubic planar maps and general planar maps are obtained. Furthermore, two known Tutte's formulae are easily deduced in the paper.     

Chromatic sum equations for rooted cubic planar maps

This paper provides a functional equation satisfied by rooted nearly cubic planar maps. By a nearly cubic map is meant such a map that all the vertices have valency 3 with the exception of at most the root-vertex. And, as a consequence, the corresponding functional equation for rooted cubic planar maps is found.     

Simplification of formulas for the number of maps on surfaces

Two combinatorial identities obtained by the author are used to simplify formulas for the number of general rooted cubic planar maps, for the number of g-essential maps on surfaces of small genus, and also for rooted Eulerian maps on the projective plane. Besides, an asymptotics for the number of maps with a large number of vertices is obtained.     

有根无环欧拉地图的数目

本文首先解决了有根无环欧拉地图依边数的三次计数方程的求解问题,同时提供一种有效的计数方法对先前的一些相关结果及其推导过程进行了必要的改进．     

The number of rooted nearly cubicC-nets

This paper provides the parametric expressions satisfied by the enumerating functions for rooted nearly cubicc-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. This Research is supported by National Natural Science Foundation of China (No. 19831080).     

Stack words, standard Young tableaux, permutations with forbidden subsequences and planar maps

Stack words stem from studies on stack-sortable permutations and represent classical combinatorial objects such as standard Young tableaux, permutations with forbidden sequences and planar maps. We extend existing enumerative results on stack words and we also obtain new results. In particular, we make a correspondence between nonseparable 3×n rectangular standard Young tableaux (or stack words where elements satisfy a ‘Towers of Hanoi’ condition) and nonseparable cubic rooted planar maps with 2n vertices enumerated by 2ⁿ(3n)!/((2n+1)!(n+1)!). Moreover, these tableaux without two consecutive integers in the same row are in bijection with nonseparable rooted planar maps with n+1 edges enumerated by 2(3n)!/((2n+1)!(n+1)!).