An Erdős-Ko-Rado Theorem For Signed Sets

A signed r-set on [n] = {1,…,n} is a pair (A, f), where A [n] is an r-set and f is a function from A to {−1, 1}. A family of signed r-sets is intersecting if for any (A, f), (B, g) there exists x A ∩ B such that f(x) = g(x). In this note, we prove that if is an intersecting family of signed r-sets on [n], then ≤ 2r−1 (r−1n−1). We also present an application of this result to a diameter problem in the grid.