Large non-trivial t-intersecting families of signed sets

For positive integers n, r, k with n > r and k > 2, a set {(x(1), y(1)), (x(2), y(2)), . . ., (x(r), y(r))} is called a k -signed r -set on [n] if x(1), ... , x(r) are distinct elements of [n] and y(1), ... , y(r) E [k]. We say that a t -intersecting family consisting of k -signed r -sets on [n] is trivial if each member of this family contains a fixed k -signed t -set. In this paper, we determine the structure of large maximal non -trivial t -intersecting families of k -signed r -sets. In particular, we characterize the non -trivial t -intersecting families with maximum size for t >= 2, extending a Hilton -Milner -type result for signed sets given by Borg.