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 G -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 ≤ b v , s ≠ b v − 1 , s , t  are non-negative integers } , where b v = v ( v − 1 ) / 8 . We establish that, for any positive integer v ≡ 0 , 1 ( mod 8 ) and v ≥ 8 , Fin ( v ) = Adm ( v ) .