The intersection problem for kite-GDDs

Abstract

In this paper the intersection problem for a pair of kite-GDDs of type $4^u$ is investigated.
The intersection problem for
kite-GDDs is the determination of all pairs $(T,s)$ such that there exists a pair of kite-GDDs $(X,{\cal H},{\cal B}_1)$ and $(X,{\cal
H},{\cal B}_2)$ of the same type $T$ is said to intersect in $s$
blocks if $|{\cal B}_1\cap {\cal B}_2|=s$.
Let $J(u)=\{s:$ $\exists$ a pair of kite-GDDs of type $4^u$
intersecting in $s$ blocks$\}$; $I(u)=\{0,1,\ldots,b_{u}-2,b_{u}\}$,
where $b_u=2u(u-1)$ is the number of blocks of an kite-GDD of type $4^u$.
We show that for any positive
integer $u\geq 3$, $J(u)=I(u)$.