Abstract
Necessary conditions, and necessary and sufficient conditions for α-resolvable are derived in terms of the characteristic roots of NN', where N is the incidence matrix of the design. A general necessary condition for the α-resolvability of an incomplete block design is also obtained. Furthermore, it is shown that there does not exist an affine α-resolvable m-associate partially balanced incomplete block (PBIB) design of regular type for m_??_2. Some applications of those necessary and sufficient conditions are further given.
