串联双路图的亏格分布

计算双路图的亏格分布是拓扑图论关注的一个问题,利用传递矩阵与向量积矩阵,给出了两类由双路图串联构建而成的两类闭链图的亏格分布.     

不可定向曲面上的最大亏格嵌入和最小亏格嵌入

研究了不可定向曲面上最大亏格嵌入的估计数,得到了几类图的指数级不可定向最大亏格嵌入的估计数的下界.利用电流图理论,证明了完全图K_(12s)在不可定向曲面上至少有2~(3s-1)个最小亏格嵌入;完全图K_(12s+3)在不可定向曲面上至少有2~(2s)个最小亏格嵌入;完全图K_(12s+7)在不可定向曲面上至少有2~(2s+1)个最小亏格嵌入.     

Genus and cancellation

In [14] we established a relationship between genus and localization of finitely generated torsion-free abelian by finite groups aud grnus and localization integral representation theory. In this paper we strrcly the consequences of this relationship. We prove results about the genus of groups which are analogues to results in integral representaion theory. In particular we prove non-cancellation phenomena for finitely generated groups with finite commutator subgroups.     

根点自粘合后图的亏格分布

利用删点、加边原理,多种乘法法则,自粘合定理给出了一个双根图在其中一个根点的度为任意大的情形下根点自粘合后图的亏格分布,推广了Gross在文[Genus distribution of graph amalgamations:self-pasting at root-vertices,Aust.J.Comb.,2011,49:19-38]中两个根点度均为2的类似结果.     

Genus Distributions of Moebius Ladders

The genus distribution of a graph is a polynomial whose coefficients are the partition of the number of embeddings with respect to the genera. In this paper,the genus distribution of Moebius ladders is provided which is an infinite class of 3-connected simple graphs.     

The Symmetric Genus of p-Groups

Let G be a finite group. The symmetric genus σ(G) is the minimum genus of any Riemann surface on which G acts. We show that a non-cyclic p-group G has symmetric genus not congruent to 1(mod p ³) if and only if G is in one of 10 families of groups. The genus formula for each of these 10 families of groups is determined. A consequence of this classification is that almost all positive integers that are the genus of a p-group are congruent to 1(mod p ³). Finally, the integers that occur as the symmetric genus of a p-group with Frattini-class 2 have density zero in the positive integers.     

Genus of the Torus Knot

In this paper,we give a metheod to obtain genus of the torus knot by some regular projection of the torus knot and have proved that the penus of the torus knot of type p,q is(p-1)(q-1).     

Maximum Genus of Strong Embeddings

The strong embedding conjecture states that any 2-connected graph has a strong embedding on some surface. It implies the circuit double cover conjecture: Any 2-connected graph has a circuit double cover.Conversely, it is not true. But for a 3-regular graph, the two conjectures are equivalent. In this paper, a characterization of graphs having a strong embedding with exactly 3 faces, which is the strong embedding of maximum genus, is given. In addition, some graphs with the property are provided. More generally, an upper bound of the maximum genus of strong embeddings of a graph is presented too. Lastly, it is shown that the interpolation theorem is true to planar Halin graph.     

一般梯图的亏格分布

本文求出了-些曲面集的亏格分布的显式表达式.在联树的基础上,通过运用曲面分类法把一般梯图的亏格分布转化为这些曲面集的线性组合,从而可求出它们的显式表达式.     

Genus expansion of HOMFLY polynomials

In the planar limit of the’ t Hooft expansion, the Wilson-loop vacuum average in the three-dimensional Chern-Simons theory (in other words, the HOMFLY polynomial) depends very simply on the representation (Young diagram), H_R(A|q)|_q=1 = (σ₁(A)^|R|. As a result, the (knot-dependent) Ooguri-Vafa partition function $\sum\nolimits_R {H_{R\chi R} \left\{ {\bar pk} \right\}}$ becomes a trivial τ -function of the Kadomtsev-Petviashvili hierarchy. We study higher-genus corrections to this formula for H_R in the form of an expansion in powers of z = q ? q^?1. The expansion coefficients are expressed in terms of the eigenvalues of cut-and-join operators, i.e., symmetric group characters. Moreover, the z-expansion is naturally written in a product form. The representation in terms of cut-and-join operators relates to the Hurwitz theory and its sophisticated integrability. The obtained relations describe the form of the genus expansion for the HOMFLY polynomials, which for the corresponding matrix model is usually given using Virasoro-like constraints and the topological recursion. The genus expansion differs from the better-studied weak-coupling expansion at a finite number N of colors, which is described in terms of Vassiliev invariants and the Kontsevich integral.     

Polyhedral Suspensions of Arbitrary Genus

A new class of polyhedra is discovered—bipyramids of arbitrarily prescribed genus. A two-dimensional generalization of Fáry’s Theorem is established. A purely combinatorial definition of a polyhedral suspension is given. A new regular two-dimensional polyhedron is constructed in four dimensions.     

Conditional distributions of record values and characterizations of distributions

We consider some regression relations for record values X(n), n > 0, generated by a sequence of independent random variables X₁, X₂, X₃,... with a common continuous cumulative distribution function F(x). New characterizations of distributions based on regression properties of record values are obtained. Bibliography: 7 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 339, 2006, pp. 5–14.     

Sequences of elliptical distributions and mixtures of normal distributions

Two conditions are shown under which elliptical distributions are scale mixtures of normal distributions with respect to probability distributions. The issue of finding the mixing distribution function is also considered. As a unified theoretical framework, it is also shown that any scale mixture of normal distributions is always a term of a sequence of elliptical distributions, increasing in dimension, and that all the terms of this sequence are also scale mixtures of normal distributions sharing the same mixing distribution function. Some examples are shown as applications of these concepts, showing the way of finding the mixing distribution function.     

Approximation of aggregate claims distributions by compound poisson distributions

New error bounds are derived for the approximation of aggregate claims distributions by compound Poisson distributions. These approximations can be recommended in most cases in which the normal approximation fails.     

Multivariate cauchy distributions as locally gaussian distributions

In the present paper, we propose a definition of locally Gaussian probability distributions of random vectors based on the linearization of their conditional quantiles. We prove that the Cauchy distribution inR ⁿ is locally Gaussian and give explicit formulas for the vectors of expectations and covariance matrices of locally Gaussian approximations. We show that locally Gaussian approximations with different dimensionalities are in some sense compatible: all of them have equal corresponding correlation coefficients. For the Cauchy distribution in a Hilbert space we prove a limit theorem on the convergence of squared finite-dimensional conditional quantiles to the stable Lévy distribution. Proceedings of the XVI Seminar on Stability Problems for Stochastic Models. Part II. Eger, Hungary, 1994.     

Genus of elements of orthogonal groups

It is proved that the number of classes in the genus of an element of an orthogonal group can take arbitrarily large values.Translated from Matematicheskie Zametki, Vol. 13, No. 5, pp. 695–702, May, 1973.The author an gratful to V. P. platonov for a number of essential remarks during performance of the present research     

On a new system of discrete distributions and characterizations of several discrete distributions by equality of distributions

This paper deals with a new system of discrete distributions. It also gives several characterizations of the Waring (and hence the Yule) distribution (and its truncated versions), the super-Poisson, the discrete uniform and other discrete distributions by using this system and other such systems existing in the literature, and linear regression. Continuous analogues of the above results are also briefly discussed.     

Operator-selfdecomposable distributions as limit distributions of processes of Ornstein-Uhlenbeck type

Processes of Ornstein-Uhlenbeck type on $\text{R}$^d are analogues of the Ornstein-Uhlenbeck process on $\text{R}$^d with the Brownian motion part replaced by general processes with homogeneous independent increments. The class of operator-selfdecomposable distributions of Urbanik is characterized as the class of limit distributions of such processes. Continuity of the correspondence is proved. Integro-differential equations for operator-selfdecomposable distributions are established. Examples are given for null recurrence and transience of processes of Ornstein-Uhlenbeck type on $\text{R}$¹.