The fine triangle intersection problem for kite systems

In this paper, we introduce the concept of the fine triangle intersection problem for a pair of GG-designs, and we consider this problem for kite systems. Let Fin(v)={(s,t):∃ a   pair of kite systems of order v intersecting in s blocks and t+s triangles}. Let Adm(v)={(s,t):s+t≤bv,s≠bv−1,s,t are non-negative integers}, where bv=v(v−1)/8bv=v(v−1)/8. We establish that, for any positive integer v≡0,1(mod8) and v≥8v≥8, Fin(v)=Adm(v).