Proof of a monotonicity conjecture

If pk(P) is the number of integer partitions of k⩾1 whose parts lie in P, it is shown that pk(P) is an increasing function of k for P={n,n+1,…,2n−1}, where n⩾3 is odd. This completes the classification of all such monotonic P with min(P)≠2,3, or 5.