NOTE ON INDEPENDENT SETS IN STEINER SYSTEMS

A partial Steiner (n, k, l)-system or briefly (n, k, l)-system is a pa ir (V, S), where V is an n-set and S is a collection of k-subsets of V , such that every I-subset of V is contained in at most one k-subset o f S. A subset X subset-of V is called independent if [X]k and S = 0. T he size of the largest independent set in S is denoted by alpha(S). De fine f(n, k, l) = min{alpha(S), S is a (n, k, l)-system}. The purpose of this note is to prove that for every k, 1, k > l cn(k-l/k-l)(log n) 1/k-1 less-than-or-equal-to f(n, k, l) less-than-or-equal-to dn(k-l/k- 1)(log n)1/k-1 holds, where c, d are positive constants depending on k and l only. (C) 1994 John Wiley & Sons, Inc.