Cyclic Group Divisible Designs

Abstract

New cyclic solutions of several group divisible incomplete block designs arc presented, A new group divisible desian is reported whose solution is also cyclic. We also present non-isomorphic solutions of several group divisible designs listed in the catalogue of Clatworthy (1973).

Partial Cyclic Solution of a 2 – (p2, p, 1) Design

“…Here a resolvable partial cyclic solution of 2-(p2,p, 1) and SRGD designs with parameters: v=b=p2, r=k=p, λ1=0, λ2=1, m=n=p for a prime p are obtained. For these resolvable designs, partial cyclic solutions are not reported in the literature; see Kageyama [5], Clatworthy [1] , Dey and Nigam [3] , Mukerjee et al [8] , Hall [4] , Dey and Balasubramanian [2] , Midha and Dey [7] , Mathon and Rosa [6] , among others. SRX numbers are from Clatworthy [1] and |1↔p⟺1→2, 2→3, …,|p-1→p, p→1. The symbol T ( α ) denotes the reference number α in the Takeuchi’s table [9] .…”

“…for a prime p are obtained. For these resolvable designs, partial cyclic solutions are not reported in the literature; see Kageyama [5], Clatworthy [1] , Dey and Articles Nigam [3] , Mukerjee et al [8] , Hall [4] , Dey and Balasubramanian [2] , Midha and Dey [7] , Mathon and Rosa [6] , among others. SRX numbers are from Clatworthy [1] and 1…”