Intersecting families, signed sets, and injection

Abstract

Let k, r, n ≥ 1 be integers, and let S n,k,r be the family of r-signed k-sets on [n] = {1, . . . , n} given byA well-known result (first stated by Meyer and proved using different methods by Deza and Frankl, and Bollobás and Leader) states that ifWe provide a proof of this result by injection (in the same spirit as Frankl and Füredi's and Hurlbert and Kamat's injective proofs of the Erdős-Ko-Rado Theorem, and Frankl's and Hurlbert and Kamat's injective proofs of the Hilton-Milner Theorem) whenever r ≥ 2 and 1 ≤ k ≤ n/2, leaving open only some cases when k ≤ n.