Publication at Faculty of Mathematics and Physics |
2020
Abstract
Let k, r, n >= 1 be integers, and let S-n,S-k,S-r be the family of r-signed k-sets on [n] = {1, ..., n} given by S-n,S-k,S-r = {{(x(1), ..., a(1)), ..., (x(k), a(k))} : {x(1), ..., x(k)} is an element of (([n])(k)), a(1), ..., a(k) is an element of [r]}. A family A subset of S-n,S-k,S-r is intersecting if A, B is an element of A implies A boolean AND B not equal empty set.
A well-known result (first stated by Meyer and proved using different methods by Deza and Frankl, and Bollobds and Leader) states that if A subset of S-n,S-k,S-r is intersecting, r >= 2 and 1 = 2 and 1 <= k <= n/2, leaving open only some cases when k <= n.