An Erdös-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 A of signed r-sets is intersecting if for any (A, f), (B, g) ∈ A there exists cursive Greek chi ∈ A ∩ B such that f(cursive Greek chi) = g(cursive Greek chi). In this note, we prove that if A is an intersecting family of signed r-sets on [n], then \A\ < 2r-1 (n-1 r-1). We also present an application of this result to a diameter problem in the grid.

Publication Title

Computers and Mathematics with Applications