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arXiv · 1212.4370

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

Filippo Disanto·Laurent Imbert·Fabrice Philippe
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Abstract

A $(p,q)$-ary chain is a special type of chain partition of integers with parts of the form $p^aq^b$ 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.

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Filippo Disanto, Laurent Imbert, Fabrice Philippe. 2013-10-22. On the maximal weight of $(p,q)$-ary chain partitions with bounded parts. https://arxiv.org/abs/1212.4370

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