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

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

2010-10-26

arxiv.org/abs/1010.5485v1

Mathematics

Combinatorics

11 pages

Scientific paper

Motivated by an error-correcting generalization of Bachet's weights problem, we define, classify and enumerate "relaxed r-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. The enumeration of the minimal such partitions (those with fewest possible parts) can be achieved by the generating functions for (r+1)-ary partitions. This generalizes work of Park on classifying r-complete partitions and that of Rodseth on enumerating minimal r-complete partitions.

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