“装错信封问题”数学模型的求解及推广

本文给出了全错位排列问题数学模型的通解，全错位排列推广问题的通解．     

环形排列计数的一种方法

对于n种不同颜色的球的重集S＝｛m1·b1,m2·b2,…,mn·bn｝,其中球bj有mj个,（j＝1,2,…,n）,Σmj＝m,把S中所有的球进行线排列有种排列方法,但把S中所有球进行环形排列（简称对S进行环形排列）情况就复杂得多．我们定义了循环节,给出了计算环形排列方式数CP（m1,m2,…mn）的递归方法．定义一个环形排列（不妨以顺时针方向看）,以K≥1个（α1,α2,…,αj）组成,称（α1,α2,…αj）为一个循环节,j为此循环节长．当（α1,α2,…αj）不能再分为2个或2个以上循环节时,称此循环节为不可分的．若某环形排列只有一…     

排列、组合应用问题

排列与组合是解决计数问题的一种强有力的工具．由于组合数学逐渐受到人们的青睐，因此，排列、组合的应用越来越广泛． 对于排列、组合应用问题，首先要分清元素与位置的关系，特殊元素和特殊位置要优先考虑．对于含有多个约束条件的排列、组合应用问题，往往以一个约束条件为主进行讨论．     

排列游戏问题及其数学表达

利用排列逆序数定理讨论两个排列游戏问题,否定了其操作的可行性．并就其中一个问题作了一般性研究,给出了该类型游戏是否可行的充要条件,更进一步得出了完成该类游戏的最少操作次数及其变式问题的可行性操作次数．在此基础上,导出一个关于矩阵的命题．     

全错位排列

定义 编号为1、2、3、…、n的n个元素a1,a2,a3,…,an分别排编号为1、2、3、…、n的n个位置,要求元素ai（i=1,2,…,n）不能排在与其对应的第i个位置,这样的排列称为n个元素的全错位排列;所有排列的个数称全错位排列数.     

随机排列方法检验方差变点

给出了随机排列的主要性质及证明。构造了随机排列检验方差变点的统计量。以GARCH(1,1)过程为例,模拟比较了随机排列方法与近似极限分布方法关于方差变点检验的临界值。应用随机排列方法检测人民币兑美元汇率的变点,并与惩罚对比函数方法作比较。模拟与实证结果均表明随机排列方法检验方差变点是灵活有效的。     

限位全排列刍议

高中数学教材,排列组合的教学是个难点。关于这部分内容,在许多资料里都编选有如下面定义的“限位全排列”问题。其中,部分元素“必在”特位的全排列,教材仅于习题中编     

一个特殊可重复排列数的算法

研究一类特殊的可重复排列性质,建立了一般情形下求这类排列数的递推公式,导出了一些特殊情形下的具体计算公式.     

排列与组合问题

基本知识加法原理 ,乘法原理 ,排列数公式 ,组合数公式 ,组合数的性质 (见高中代数课本第九章 ) .2　应用举例排列与组合问题 ,通常要应用加法原理和乘法原理 ,由于这两个原理容易发生混淆 ,我们应特别注意加法原理中每类办法都是相互独立的 ,不受其它类办法的制约 ,而乘法原理中的ｎ个步骤是一环接一环 ,缺一不可的 ;排列与组合的区别就在于前者强调了元素的顺序 ,不同的顺序决定不同的排列 ,而后者与元素顺序无关 .例 1　学校开设语文 ,外语 ,政治 ,体育 ,数学 ,物理 ,化学七门课程 .1)一天开设七门不同课程 ,体育不排在第一节 ,也不排…     

考查素质教育的好指挥棒：2001年理（20）题试卷评析

20 0 1年理 (2 0 )题是一道考查排列、组合、二项式定理、不等式的基本知识和逻辑推理能力的证明题 .由于近十几年来关于排列、组合和二项式定理内容仅限于考选择题和填空题 ,从未出现过证明题 .因此中学教师未对学生进行类似题目的演练 ,甚至教师有些话误导了学生或限制了学生的思维 .面对新型试题 ,学生感到措手不及而无从下手 .尽管今年高考数学成绩比往年略有提高 ,但此题得分率仅为 2 7% ,得 0分者达 40 % ,得 2分者占 3 0 % ,而得 1 0分以上者不足 1 % ,得满分 (1 2分 )者不足 0 1 % .其实这并不是一道难题 ,如果考生具备基本的排列…     

The diffeomorphic types of the complements of arrangements in CP~3Ⅱ

For any arrangement of hyperplanes in CP~3,we introduce the soul of this arrangement. The soul,which is a pseudo-complex,is determined by the combinatorics of the arrangement of hyper- planes.In this paper,we give a sufficient combinatoric condition for two arrangements of hyperplanes to be diffeomorphic to each other.In particular we have found sufficient conditions on combinatorics for the arrangement of hyperplanes whose moduli space is connected.This generalizes our previous result on hyperplane point arrangements in CP~3.     

The diffeomorphic types of the complements of arrangements in ??3 II

For any arrangement of hyperplanes in ℂℙ³, we introduce the soul of this arrangement. The soul, which is a pseudo-complex, is determined by the combinatorics of the arrangement of hyperplanes. In this paper, we give a sufficient combinatoric condition for two arrangements of hyperplanes to be diffeomorphic to each other. In particular we have found sufficient conditions on combinatorics for the arrangement of hyperplanes whose moduli space is connected. This generalizes our previous result on hyperplane point arrangements in ℂℙ³. This work was partially supported by NSA grant and NSF grant     

Discriminantal Arrangements, Fiber Polytopes and Formality

Manin and Schechtman defined the discriminantal arrangement of a generic hyperplane arrangement as a generalization of the braid arrangement. This paper shows their construction is dual to the fiber zonotope construction of Billera and Sturmfels, and thus makes sense even when the base arrangement is not generic. The hyperplanes, face lattices and intersection lattices of discriminantal arrangements are studied. The discriminantal arrangement over a generic arrangement is shown to be formal (and in some cases 3–formal), though it is in general not free. An example of a free discriminantal arrangement over a generic arrangement is given.     

Partial parking functions

We characterise the Pak–Stanley labels of the regions of a family of hyperplane arrangements that interpolate between the Shi arrangement and the Ish arrangement.     

The double Coxeter arrangement

Let V be Euclidean space. Let be a finite irreducible reflection group. Let be the corresponding Coxeter arrangement. Let S be the algebra of polynomial functions on V. For choose such that . The arrangement is known to be free: the derivation module is a free S-module with generators of degrees equal to the exponents of W. In this paper we prove an analogous theorem for the submodule of defined by . The degrees of the basis elements are all equal to the Coxeter number. The module may be considered a deformation of the derivation module for the Shi arrangement, which is conjectured to be free. The proof is by explicit construction using a derivation introduced by K. Saito in his theory of flat generators. Received: March 13, 1997     

Parameterized algorithmics for linear arrangement problems

We discuss different variants of linear arrangement problems from a parameterized perspective. More specifically, we concentrate on developing simple search tree algorithms for these problems. Despite this simplicity, the analysis of the algorithms is often rather intricate. For the newly introduced problem linear arrangement by deleting edges, we also show how to derive a small problem kernel.     

An Algorithm for Reducibility of 3-arrangements

We consider a central hyperplane arrangement in a three-dimensional vector space. The definition of characteristic form to a hyperplane arrangement is given and we could make use of characteristic form to judge the reducibility of this arrangement. In addition, the relationship between the reducibility and freeness of a hyperplane arrangement is given     

Linear arrangement problems on recursively partitioned graphs

We analyze the complexity of the restrictions of linear arrangement problems that are obtained if the legal permutations of the nodes are restricted to those that can be obtained by orderings of a binary tree structuring the nodes of the graph, the so-called p-tree. These versions of the linear arrangement problems occur in several places in current circuit layout systems. There the p-tree is the result of a recursive partitioning process of the graph. We show that the MINCUT LINEAR ARRANGEMENT problem and the OPTIMAL LINEAR ARRANGEMENT problem can be solved in polynomial time, if the p-tree is balanced. All other versions of the linear arrangement problems we analyzed are NP-complete.     

Between Shi and Ish

We introduce a new family of hyperplane arrangements in dimension $n\ge 3$ that includes both the Shi arrangement and the Ish arrangement. We prove that all the members of a given subfamily have the same number of regions – the connected components of the complement of the union of the hyperplanes – which can be bijectively labeled with the Pak–Stanley labeling. In addition, we show that, in the cases of the Shi and the Ish arrangements, the number of labels with reverse centers of a given length is equal, and conjecture that the same happens with all of the members of the family.     

Signed graphs and the freeness of the Weyl subarrangements of type Bℓ

A Weyl arrangement is the hyperplane arrangement defined by a root system. Saito proved that every Weyl arrangement is free. The Weyl subarrangements of type $A_{\ell }$ are represented by simple graphs. Stanley gave a characterization of freeness for this type of arrangements in terms of their graph. In addition, the Weyl subarrangements of type $B_{\ell }$ can be represented by signed graphs. A characterization of freeness for them is not known. However, characterizations of freeness for a few restricted classes are known. For instance, Edelman and Reiner characterized the freeness of the arrangements between type $A_{\ell -1}$ and type $B_{\ell }$. In this paper, we give a characterization of the freeness and supersolvability of the Weyl subarrangements of type $B_{\ell }$ under certain assumption.