$A(n,k)$和$P(n,k)$的精确公式

设A(n,k)表示不定方程的非负整数解的个数,P(n,k)为整数n分为k个部分的无序分拆的个数,每个分部不小于1．本文给出了A(n,k)和P(n,k)的精确表达式．     

Semi-symmetric solutions for (n,k) games

The concept of semi-symmetric solution for (n, k) games was presented byMuto [1978]. An extension of this type of solution is studied here.     

Symmetric solutions for (n,k) games

Symmetric solutions (or symmetric stable sets) and their uniqueness are investigated for some classes of symmetric,n-person, cooperative games in characteristic function form known as (n, k) games.     

An algorithm for computingSU(n) invariants

An algorithm and its computer implementation for calculating the values of three types of invariants in any irreducible representation ofSU(n) are described. It is not necessary to calculate the structure constants or the matrix elements of generators. Computing times forn10 are quite reasonable.     

Factorization theorem for the dimension (m, n)-dim

A factorization theorem for the dimension (m,n)-dim is proved.     

An O(n log n) algorithm for finding all repetitions in a string

Any nonempty string of the form xx is called a repetition. An O(n log n) algorithm is presented to find all repetitions in a string of lenght n. The algorithm is based on a linear algorithm to find all the new repetitions formed when two strings are concatenated. This linear algorithm is possible because new repetitions of equal length must occur in blocks with consecutive starting positions. The linear algorithm uses a variation of the Knuth-Morris-Pratt algorithm to find all partial occurrences of a pattern within a text string. It is also shown that no algorithm based on comparisons of symbols can improve O(n log n). Finally, some open problems and applications are suggested.     

Estimates of the dimension (m, n)-dim

The dimension (m,n)-dim is estimated by means of the Lebesgue dimension.     

On strictly Deza graphs with parameters (n,k,k−1,a)

A non-empty $k$-regular graph $\Gamma$ on $n$ vertices is called a Deza graph if there exist constants $b$ and $a$ $(b\ge a)$ such that any pair of distinct vertices of $\Gamma$ has either $b$ or $a$ common neighbours. The quantities $n$, $k$, $b$, and $a$ are called the parameters of $\Gamma$ and are written as the quadruple $(n,k,b,a)$. If a Deza graph has diameter 2 and is not strongly regular, then it is called a strictly Deza graph. In the present paper, we investigate strictly Deza graphs whose parameters $(n,k,b,a)$ satisfy the conditions $k=b+1$ and $\frac{k(k-1)-a(n-1)}{b-a}>1$.     

线形(n,f,k)系统和系统的可靠度计算新方法

本文应用两端同时进行的有限马尔可夫链嵌入法给出了具有复合失效准则的(n,f,k)系统和系统可靠度计算公式及公式中连接矩阵的结构特点。数值计算结果表明,随着构成系统的单元个数的增加,应用两端同时进行的有限马尔可夫链嵌入法比应用传统的有限马尔可夫链嵌入法计算可靠度能节省大量运算时间,特别是对于具有对称结构的(n,f,k)和系统效果更加明显。     

On B(n,k) 2-groups

A finite group G is said to be a B(n, k) group if for any n-element subset {a ₁,…, a _n } of G, |{a _i a _j |1 ≤ i, j ≤ n}| ≤k. In this article, we give characterizations of the B(5, 19) 2-groups, and the B(6, k) 2-groups for 21 ≤ k ≤ 28.     

An O(n) algorithm for quadratic knapsack problems

An algorithm is presented which solves bounded quadratic optimization problems with n variables and one linear constraint in at most O(n) steps. The algorithm is based on a parametric approach combined with well-known ideas for constructing efficient algorithms. It improves an O(n log n) algorithm which has been developed for a more restricted case of the problem.