The intersection problem for PBD(5*,3)sPBD(5*,3)s

For every v≡5v≡5(mod6) there exists a pairwise balanced design   (PBD) of order vv with exactly one block of size 5 and the rest of size 3. We will refer to such a PBD as a PBD(5*,3)PBD(5*,3). A flower in a PBD(5*,3)PBD(5*,3) is the set of all blocks containing a given point. If (S,B)(S,B) is a PBD(5*,3)PBD(5*,3) and F   is a flower, we will write F*F* to indicate that F contains the block of size 5.The intersection problem   for PBD(5*,3)PBD(5*,3)s is the determination of all pairs (v,k)(v,k) such that there exists a pair of PBD(5*,3)PBD(5*,3)s (S,B1)(S,B1) and (S,B2)(S,B2) of order v containing the same block b   of size 5 such that |(B1⧹b)∩(B2⧹b)|=k|(B1⧹b)∩(B2⧹b)|=k.The flower intersection problem   for PBD(5*,3)PBD(5*,3)s is the determination of all pairs (v,k)(v,k) such that there exists a pair of PBD(5*,3)PBD(5*,3)s (S,B1)(S,B1) and (S,B2)(S,B2) of order v   having a common flower F*F* such that |(B1⧹F*)∩(B2⧹F*)|=k|(B1⧹F*)∩(B2⧹F*)|=k.In this paper we give a complete solution of both problems.