On $\alpha$-Resolvability and Affine $\alpha$-Resolvability of Incomplete Block Designs

Abstract

A necessary condition for the $\alpha$-resolvability of an incomplete block design is obtained. Further, a necessary and sufficient condition for an $\alpha$-resolvable incomplete block design to be affine $\alpha$-resolvable is obtained in terms of the largest characteristic root of $NN'$ other than $rk$, where $N$ is the incidence matrix of the design.