Exponents of Uniform L-Systems

Let L/[0, k&1]. A family F is called an (n, k, L)-system (or (k, L)system, L-system for short) if F/( [n] k ) and |F & F$| # L holds for all distinct F, F$ # F. Define m(n, k, L) :=max[ |F | : F is (n, k, L)-system]. If there exist constants c, c$, : depending only on k and L, and satisfying cn<m(n, k, L)<c$n, then we define :(k, L) :=: which is called the exponent of (k, L)-system. Conjecture 1. For all k and L, :(k, L) exists. article no. 0061