A Kruskal-Katona type theorem for integer partitions

Let N be the set of positive integers, and let P(n)=⋃1≤l≤n{(x1,…,xl)∈Nl:x1+⋯+xl=n} be the set of (ordered) partitions of n. We show that there exist a rank function and orderings ≤c and ≺ such that the ranked poset (P(n),≤c,≺) is Macaulay.