On Resolvable and Affine Resolvable Variance-Balanced Designs
本文定义了仿射可分解性概念，并研究了它与方差平衡及块数关系b=v+t-1之间的逻辑关联，给出了某些条件下三者等价的条件及不存在性结果，最后提出一个与因子设计相关的开放问题。
This paper introduces the notion of affine (μ1, …, μ1)-resolvability and explores the interrelations between: (a) affine (μ1…, μ1)-resolvability, (b) variance-balance, and (c) the relation b = v+t−1, where b is the number of blocks. It is seen that, while (a) and (b) imply (c), and (b) and (c) imply (a), the relation (a) and (c) imply (b) is not in general true. A necessary and sufficient condition under which (a) and (c) imply (b) has been derived and certain nonexistence results follow. The last section states an open problem in this connexion and indicates the link with a problem in factorial designs.