On the Cameron-Praeger conjecture

This paper takes a significant step towards confirming a long-standing and far-reaching conjecture of Peter J. Cameron and Cheryl E. Praeger. They conjectured in 1993 that there are no non-trivial block-transitive 6-designs. We prove that the Cameron-Praeger conjecture is true for the important case of non-trivial Steiner 6-designs, i.e. for 6-(v,k,λ) designs with λ=1, except possibly when the group is PΓL(2,pe) with p=2 or 3, and e is an odd prime power.     

An Erdös-Ko-Rado theorem for restricted signed sets

A restricted signed r-set is a pair （A, f）, where A lohtain in [n] = {1, 2,…, n} is an r-set and f is a map from A to [n] with f（i） ≠ i for all i ∈ A. For two restricted signed sets （A, f） and （B, g）, we define an order as （A, f） ≤ （B, g） if A C B and g｜A ： f A family .A of restricted signed sets on [n] is an intersecting antiehain if for any （A, f）, （B, g） ∈ A, they are incomparable and there exists x ∈ A ∩ B such that f（x） = g（x）. In this paper, we first give a LYM-type inequality for any intersecting antichain A of restricted signed sets, from which we then obtain ｜A｜≤ （r-1^n-1）（n-1）^r-1 if A. consists of restricted signed r-sets on [n]. Unless r = n = 3, equality holds if and only if A consists of all restricted signed r-sets （A, f） such that x0∈ A and f（x0） =ε0 for some fixed x0 ∈ [n], ε0 ∈ [n] ／ {x0}.     

A decomposition theorem for G-groups

Some classical results about linear representations of a finite group G have been also proved for representations of G on non-abelian groups （G-groups）. In this paper we establish a decomposition theorem for irreducible G-groups which expresses a suitable irreducible G-group as a tensor product of two projective G-groups in a similar way to the celebrated theorem of Clifford for linear representations. Moreover, we study the non-abelian minimal normal subgroups of G in which this decomposition is possible.     

全错位排列问题的基于芯片的DNA计算模型

全错位排列问题作为组合数学中一个重要的问题,到目前为止还没有好的算法.应用DNA芯片技术,提出了全错位排列问题的基于芯片的DNA计算模型,并对模型进行了简要分析.     

关于多项式函数的计数

Polynomial functions （in particular, permutation polynomials） play an important role in the design of modern cryptosystem. In this note the problem of counting the number of polynomial functions over finite commutative rings is discussed. Let A be a general finite commutative local ring. Under a certain condition, the counting formula of the number of polynomial functions over A is obtained. Before this paper, some results over special finite commutative rings were obtained by many authors.     

Improving the complexity of chaotic sequence based on the PCA algorithm

The principal component analysis (PCA) is an effective statistical analysis method in statistical data analysis, feature extraction and data compression. The method simplifies multiple related variables into a linear combination of several irrelevant variables, through the less-comprehensive index as far as possible to replace many of the original data, and can reflect the information provided by the original data. This paper studies the signal feature extraction algorithm based on PCA, and extracts sequences’ feature which generated by Logistic mapping. Then we measured the complexity of the reconstructed chaotic sequences by the permutation entropy algorithm. The testing results show that the complexity of the reconstruction sequences is significantly higher than the original sequences.     

The probability of avoiding consecutive patterns in the Mallows distribution

We use combinatorial and probabilistic techniques to study growth rates for the probability that a random permutation from the Mallows distribution avoids consecutive patterns. The Mallows distribution is a q‐analogue of the uniform distribution weighting each permutation π by , where is the number of inversions in π and q is a positive, real‐valued parameter. We prove that the growth rate exists for all patterns and all q > 0, and we generalize Goulden and Jackson's cluster method to keep track of the number of inversions in permutations avoiding a given consecutive pattern. Using singularity analysis, we approximate the growth rates for length‐3 patterns, monotone patterns, and non‐overlapping patterns starting with 1, and we compare growth rates between different patterns. We also use Stein's method to show that, under certain assumptions on q and σ, the number of occurrences of a given pattern σ is well approximated by the normal distribution.     

改进二元分布估计算法求解置换流水车间调度问题

针对置换流水车间调度这类组合最优化问题的求解,提出了一种改进二元分布估计算法(Improved binary estimation distribution algorithm, I-EDA)。算法以二元分布估计算法为架构,使用NEH(Nawaz-Enscore-Ham)启发式算法生成初始解,提高了初始解的质量;通过对优势解的统计采样构建位置矩阵模型和链接矩阵模型,依照两个矩阵模型的合并概率组合链接区块产生子代。提出了NEH插入式重组策略和基于位置概率的交换策略和两种全新局部搜索机制替代原二元分布估计算法的相邻交换法,以进一步筛选优势解。最后通过对Reeves标准测试集的仿真实验和算法比较验证了所提出算法的有效性。