AN ERDOS-KO-RADO THEOREM FOR SIGNED SETS

A signed r-set on [n] = {1,..., n} is a pair (A, f), where A subset of [n] is an r-set and f is a function from A to {-1, 1}. A family A of signed r-sets is intersecting if for any (A, f), (B, g) is an element of A there exists x is an element of A boolean AND B such that f(x)=g( x). Tn this note, we prove that if A is an intersecting family of sign ed r-sets on [n], then \A\ less than or equal to 2(r-1)(3P:). We also present an application of this result to a diameter problem in the gri d.