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Let us say that a partition of the positive integer n represents a, 0 ≤ a ≤ n, if there is a submultiset of the multiset of the parts whose sum is a. Erdő os and Szalay have proved that almost all partitions of n represent all integers a, 0 ≤ a ≤ n. If $${\mathcal{A}}$$ is a finite set of positive integers, let us denote by p~(n, $${\mathcal{A}}$$ ) the number of partitions of n which represent...
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