An Erd?s-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.
intersecting families extremal problems discrete isoperimetric inequalities