Multiple cross-intersecting families of signed sets

Abstract: A k-signed r-set on is an ordered pair , where A is an r-subset of and f is a function from A to . Families are said to be cross-intersecting if any set in any family intersects any set in any other family . Hilton proved a sharp bound for the sum of sizes of cross-intersecting families of r-subsets of . Our aim is to generalise Hilton''s bound to one for families of k-signed r-sets on . The main tool developed is an extension of Katona''s cyclic permutation argument. [Copyright &y& Elsevier]