Perfect 2-colorings of a hypercube

A coloring of the vertices of a graph is called perfect if the multiset of colors of all neighbors of a vertex depends only on its own color. We study the possible parameters of perfect 2-colorings of the n-dimensional cube. Some necessary conditions are obtained for existence of such colorings. A new recursive construction of such colorings is found, which produces colorings for all known and infinitely many new parameter sets.     

On invertible terraces for non‐abelian groups

We give several constructions for invertible terraces and invertible directed terraces. These enable us to give the first known infinite families of invertible terrraces, both directed and undirected, for non‐abelian groups. In particular, we show that all generalized dicyclic groups of orders 24k + 4 and 24k + 20 have an invertible directed terrace and that all groups of the form A × G have an invertible terrace, where A is an (possibly trivial) abelian group of odd order and G is any one of: (i) a generalized dihedral group of order 12k + 2 or 12k + 10; (ii) a generalized dicyclic group of order 24k + 4 or 24k + 20; (iii) a non‐abelian group of order n with 10 ≤ n ≤ 21; (iv) a non‐abelian binary group of order n with 24 ≤ n ≤ 42. © 2006 Wiley Periodicals, Inc. J Combin Designs 15: 437–447, 2007     

Constructing Pandiagonal Latin Squares from Linear Cellular Automaton on Elementary Abelian Groups

The constructed pandiagonal Latin squares by Hedayat's method are cyclic. During the last decades several authors described methods for constructing pandiagonal Latin squares that are semi‐cyclic. In this article, we have applied linear cellular automaton on elements of permutation elementary abelian p‐groups, which are ordered by the lexicographic ordering, and we proposed an algorithm for constructing noncyclic pandiagonal Latin squares of order , for prime .     

Distances of group tables and latin squares via equilateral triangle dissections

Denote by gdist(p)$\mathrm{gdist}(p)$ the least non-zero number of cells that have to be changed to get a latin square from the table of addition modulo p  . A conjecture of Drápal, Cavenagh and Wanless states that there exists c>0$c>0$ such that gdist(p)?clog(p)$\mathrm{gdist}(p)?c\log (p)$. In this paper the conjecture is proved for c≈7.21$c\approx 7.21$, and as an intermediate result it is shown that an equilateral triangle of side n   can be non-trivially dissected into at most 5_log2(n)$5{\log }_2(n)$ integer-sided equilateral triangles. The paper also presents some evidence which suggests that gdist(p)/log(p)≈3.56$\mathrm{gdist}(p)/\log (p)\approx 3.56$ for large values of p.     

ρ—混合序列加权和的完全收敛性

对混合速度不作限制下，讨论了ρ－混合序列加权和Ｔｎ＝Σ（ｎ，ｋ＝１）αｎｋＸｋ的完全收敛性，推广了Ｗ．Ｆ．Ｓｔｏｕｒｔ的结果。将此新结果应用于线性模型参数β的估计中，得出β的最小二乘估计βｎ的强相合性     

在计算机模拟试验中不同试验设计的比较

计算机模拟试验的设计与建模有许多方法,本文选择了四种不同类型的真模型,用四种试验设计方法,考虑了大小不同的试验方案,并选用了四种建模方法进行比较,给出一些经验性结论,相信这些结论在计算机试验中是有参考价值的。     

Tight bounds for break minimization in tournament scheduling

We consider round-robin sports tournaments with n teams and n−1 rounds. We construct an infinite family of opponent schedules for which every home-away assignment induces at least breaks. This construction establishes a matching lower bound for a corresponding upper bound from the literature.     

立方体的线图的限制性连通度(英文)

子集SE(G)称为是图G的4-限制性边割,如果G-S不连通且每个连通分支至少有4个点.图G中基数最小的4-限制性边割称为4-限制性边连通度,记为λ4(G).本文确定了λ4(Qn)=4n-8.类似的,子集FV(G)称为图G的Rg-限制性点割,如果G-F不连通且每个连通分支的最小度不小于g.基数最小的Rg-限制性点割称为图G的Rg-限制性点连通度,记为κg(G).本文确定了κ1(L(Qn))=3n-4,κ2(L(Qn))=4n-8,其中L(Qn)是立方体的线图.     

The Existence of Mixed Orthogonal Arrays with Four and Five Factors of Strength Two

Symmetric orthogonal arrays and mixed orthogonal arrays are useful in the design of various experiments. They are also a fundamental tool in the construction of various combinatorial configurations. In this paper, we investigated the mixed orthogonal arrays with four and five factors of strength two, and proved that the necessary conditions of such mixed orthogonal arrays are also sufficient with several exceptions and one possible exception.     

Multi-criteria robust design of a JIT-based cross-docking distribution center for an auto parts supply chain

We present a solution framework based on discrete-event simulation and enhanced robust design technique to address a multi-response optimization problem inherent in logistics management. The objective is to design a robust configuration for a cross-docking distribution center so that the system is insensitive to the disturbances of supply uncertainty, and provides steady parts supply to downstream assembly plants. In the proposed approach, we first construct a simulation model using factorial design and central composite design (CCD), and then identify the models that best describe the relationship between the simulation responses and system factors. We employ the response surface methodology (RSM) to identify factor levels that would maximize system potential.