On the maximal weight of $(p,q)$-ary chain partitions with bounded parts - LIRMM - Laboratoire d’Informatique, de Robotique et de Microélectronique de Montpellier Access content directly
Journal Articles Integers : Electronic Journal of Combinatorial Number Theory Year : 2014

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

Filippo Disanto
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Laurent Imbert

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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Dates and versions

lirmm-01104898 , version 1 (22-08-2022)

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Filippo Disanto, Laurent Imbert, Fabrice Philippe. On the maximal weight of $(p,q)$-ary chain partitions with bounded parts. Integers : Electronic Journal of Combinatorial Number Theory, 2014, 14, pp.A37. ⟨lirmm-01104898⟩
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