2010/10/26 by Jorge Bruno, Bruno, Jorge, Edwin O'Shea +2
Mathematics · #05A17 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT #msc:05A17
paper · pdf · doi:10.48550/arxiv.1010.5485
14 pages, 1 figure. Major revision - main result is now shown using Brion's formula for lattice point enumeration in polyhedra
openalex publication_date 2010/10/26 · arxiv created 2014/01/08 · arxiv updated 2014/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.