A generalization of the ray‐chaudhuri‐wilson theorem

Let K = { k 1 ,…, k r } and L = { l 1 ,…, l s } be two sets of non‐negative integers and assume k i > l j for every i,j. Let F be an L ‐intersecting family of subsets of a set of n elements. Assume the size of every set in F is a number from K. We conjecture that | F | ⩽ ( n s ). We prove that our conjecturer is true for any K. (with min k i ⩾ s ) when L = {0,1,…, s − 1}. We also show that for any K and any L , (with min k i > max l j ) CALLING STATEMENT : © 1995 John Wiley & Sons, Inc.