Gruplara bölünebilen tasarımlar

This thesis is on Group Divisible Designs (GDDs), one of the main structures inCombinatorial Design Theory. GDDs were first introduced by Hanani in 1975 andwidely used in constructing other combinatorial structures such as pairwise balanceddesigns, f rames and balanced incomplete block designs since then.A GDD is a triple (X, G, B), where X is the point set, which satisfies the followingproperties:(1) G is a partition of X into subsets called groups.(2) B is a set of subsets of X (called blocks) such that a group and a block contain atmost one common point.(3) every pair of points from distinct groups occurs in a unique block.A K − GDD of type gu1 g2 2 . . . gus is a GDD where every block has size from theus1set K and there are ui groups of size gi , for i = 1, 2, . . . , s. In our study all blockshave size k. In this thesis we will present:(1) 3 − GDDs of type:(i) gu (uniform 3 − GDDs)(ii) gu m1(iii) gu 1t(iv) g1 v1 1 g(2) 4 − GDDs of type:(i) gu (uniform 4 − GDDs)(ii) gu m1 .iv