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

Filippo Disanto 1, 2 Laurent Imbert 1 Fabrice Philippe 1
1 ARITH - Arithmétique informatique
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : A (p,q)-ary chain is a special type of chain partition of integers with parts of the form paqb 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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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00815458
Contributor : Laurent Imbert <>
Submitted on : Thursday, April 18, 2013 - 4:49:19 PM
Last modification on : Wednesday, October 9, 2019 - 9:42:02 AM

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  • HAL Id : lirmm-00815458, version 1
  • ARXIV : 1212.4370

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Filippo Disanto, Laurent Imbert, Fabrice Philippe. On the maximal weight of $(p,q)$-ary chain partitions with bounded parts. 2012. ⟨lirmm-00815458⟩

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