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

Abstract

A (p,q)(p,q)-ary chain is a special type of chain partition of integers with parts of the form paqbp^aq^b for some fixed integers pp and qq. In this note, we are interested in the maximal weight of such partitions when their parts are distinct and cannot exceed a given bound mm. Characterizing the cases where the greedy choice fails, we prove that this maximal weight is, as a function of mm, asymptotically independent of max⁡(p,q)\max(p,q), and we provide an efficient algorithm to compute it.Comment: 17 page

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