The Intersection Problem for Kite-GDDs of Type $2^{u}$

Abstract:

      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 $T$ satisfying $|{\cal B}_1\cap {\cal B}_2|=s$. In this paper the intersection problem for a pair of kite-GDDs of type $2^u$ is investigated. Let $J(u)=\{s:$ $\exists$ a pair of kite-GDDs of type $2^u$ intersecting in $s$ blocks$\}$; $I(u)=\{0,1,\ldots,b_{u}-2,b_{u}\}$, where $b_u=u(u-1)/2$ is the number of blocks of a kite-GDD of type $2^u$. We show that for any positive integer $u\geq 4$, $J(u)=I(u)$ and $J(3)= \{0,3\}$.