On the maximal weight of $(p,q)$-ary chain partitions with bounded parts

A (p, q)-ary chain is a special type of chain partition of integers with parts of the form pq for some fixed integers p and q. In this note, we are interested in the maximal weight of such partitions when their parts are distinct and cannot exceed a given bound m. Characterizing the cases where the greedy choice fails, we prove that this maximal weight is, as a function of m, asymptotically independent of max(p, q), and we provide an efficient algorithm to compute it.