Relaxed complete partitions: an error-correcting Bachet's problem
Combinatorics
2014-01-09 v2 Number Theory
Abstract
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 R{\o}dseth on enumerating minimal complete partitions.
Cite
@article{arxiv.1010.5485,
title = {Relaxed complete partitions: an error-correcting Bachet's problem},
author = {Jorge Bruno and Edwin O'Shea},
journal= {arXiv preprint arXiv:1010.5485},
year = {2014}
}
Comments
14 pages, 1 figure. Major revision - main result is now shown using Brion's formula for lattice point enumeration in polyhedra