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) = f(s, t) : there exists a pair of kite systems of order a intersecting in s blocks and t + s triangles}. Let Adm(v) =[(s, t): s + t <= b(v), s not equal 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). (C) 2011 Elsevier B.V. All rights reserved.