Relaxed complete partitions: an error-correcting Bachet's problem

Motivated by an error-correcting generalization of Bachet's weights problem, we define and classify relaxed complete partitions. We show that these partitions enjoy a succinct description in terms of lattice points in polyhedra, with adjustments in the error being commensurate with translations...

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Bibliographic Details
Published in:arXiv.org 2014-01
Main Authors: Bruno, Jorge, O'Shea, Edwin
Format: Article
Language:English
Subjects:
Classification
Enumeration
Error correction
Hyperplanes
Partitions
Translations
Online Access:Get full text
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Summary:Motivated by an error-correcting generalization of Bachet's weights problem, we define and classify relaxed complete partitions. We show that these partitions enjoy a succinct description in terms of lattice points in polyhedra, with adjustments in the error being commensurate with translations in the defining hyperplanes. Our main result is that the enumeration of the minimal such partitions (those with fewest possible parts) is achieved via Brion's formula. This generalizes work of Park on classifying complete partitions and that of Rødseth on enumerating minimal complete partitions.
ISSN:2331-8422