Intersection theorems for multisets

Let kk, tt and mm be positive integers. A kk-multiset of [m][m] is a collection of kk integers from the set {1,…,m}{1,…,m} in which the integers can appear more than once. We use graph homomorphisms and existing theorems for intersecting and tt-intersecting kk-set systems to prove new results for intersecting and tt-intersecting families of kk-multisets. These results include a multiset version of the Hilton–Milner theorem and a theorem giving the size and structure of the largest tt-intersecting family of kk-multisets of an mm-set when m≥2k−tm≥2k−t.