On the E- and MV-optimality of block designs having k≥v

In this paper we consider the problem of determining and constructing E- and MV-optimal block designs to use in experimental settings where treatments are applied to experimental units occurring in b blocks of size k, k. It is shown that some of the well-known methods for constructing E- and MV-optimal unequally replicated designs having k fail to yield optimal designs in the case where . Some sufficient conditions are derived for the E- and MV-optimality of block designs having and methods for constructing designs satisfying these sufficient conditions are given.     

区传递7-(v,k,λ)设计

具有良好传递性的区组设计是代数组合学研究的一个重要领域.1993年,Cameron和Praeger证明了不存在区传递的8-设计.因此研究区传递的7-设计的存在性是一个很重要的课题.2013年,龚罗中和刘伟俊证明了不存在指数超过5的区传递7-设计.本文在此基础上证明了不存在区长小于100的区传递7-设计.     

Steinberg triality groups acting on 2 - (v, k, 1) designs

A 2 - (v,k,1) design D = (P, B) is a system consisting of a finite set P of v points and a collection B of k-subsets of P, called blocks, such that each 2-subset of P is contained in precisely one block. Let G be an automorphism group of a 2- (v,k,1) design. Delandtsheer proved that if G is block-primitive and D is not a projective plane, then G is almost simple, that is, T ≤ G ≤ Aut(T), where T is a non-abelian simple group. In this paper, we prove that T is not isomorphic to 3D4(q). This paper is part of a project to classify groups and designs where the group acts primitively on the blocks of the design.     

Some new (s,k,λ)-translation transversal designs with non-abelian translation group

For >1 and many values of s andk, we give a construction of (s,k,)-partitions of finite non-abelian p-groups and of Frobenius groups with non-abelian kernel. These groups are associated with translation transversl designs of the same parameters.     

Application of (v, k, λ)-configuration to generation of a conference key

In order for all participants at video conference to communicate mutually, the conference key should be necessary. In this paper, we present the communication protocol that generates a conference key efficiently based on (v,k,λ)-configuration, one class of block designs, which minimizes message transmission overhead needed for this key. Especially, in the case of λ=1, the protocol requires only O(v√v) messages, where v is the number of participants.     

A survey of pseudo (v,k, λ)-designs

This work is an attempt to give a complete survey of all known results about pseudo (v, k, )-designs. In doing this, the author hopes to bring more attention to his conjecture given in Section 6; an affirmative answer to this conjecture would settle completely the existence and construction problem for a pseudo (v, k, )-design in terms of the existence of an appropriate (v, k, )-design.     

A new class of symmetric (v,k, λ)-designs

We construct new families of symmetric (v, k, )-designs with parameters

P(G,λ)=sum(n/k[k,n-k](λ)_(k+l)图的刻画

应用色多项式的性质 .讨论了具有色多项式 ∑k≤ nnk　 kn - k (λ) k+l 图的结构 ,刻画了具有这种色多项式的全部色等价图 .     

Flag-transitive point-primitive 2-（v,k,4） symmetric designs and two dimensional classical groups

Let D be a 2-(v, k, 4) symmetric design and G be a flag-transitive point-primitive automorphism group of D with X ⊴ G ≤ Aut(X) where X ≅ PSL ₂(q). Then D is a 2-(15, 8, 4) symmetric design with X = PSL ₂(9) and X _x = PGL ₂(3) where x is a point of D.     

On the Solvability of x∈Ax＋λBx in a General Cone with A and B Multivalued k－set－contractive

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Existence of Simple OA_λ(3,5,v)′s

An orthogonal array of strength t,degree k,order v and index λ,denoted by OAλ(t,k,v),is a λvt× k array on a v symbol set such that each λvt× t subarray contains each t-tuple exactly λ times.An OAλ(t,k,v) is called simple and denoted by SOAλ(t,k,v)if it contains no repeated rows.In this paper,it is proved that the necessary conditions for the existence of an SOAλ(3,5,v) with λ≥ 2 are also sufficient with possible exceptions where v = 6 and λ∈ {3,7,11,13,15,17,19,21,23,25,29,33}.     

Lie comodules and the constructions of Lie bialgebras

In this paper,we first give a direct sum decomposition of Lie comodules,and then accord- ing to the Lie comodule theory,construct some(triangular)Lie bialgebras through Lie coalgebras.