Name
Abstract | ||
|---|---|---|
We examine a version of the Universal Number Partition Problem with a divisibility property referred to as the Universal Shelf Packing Problem (USPP). We show that if a shelf length is a product of powers of two primes the USPP is always partitionable. In the case where the shelf length is a product of three distinct primes we propose an efficient scheme to determine when such a case is not partitionable. We also show that a shelf length that is a product of powers of four or more primes always has at least one partition failure. Our analysis uses elementary number theory, known results related to the linear Diophantine Frobenius problem, and a new result on Frobenius gaps. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1016/j.disc.2012.01.022 | Discrete Mathematics |
Keywords | Field | DocType |
frobenius problem,integer partitions,packing | Partition problem,Discrete mathematics,Combinatorics,Coin problem,Packing problems,Divisibility rule,Partition (number theory),Diophantine equation,Number theory,Mathematics | Journal |
Volume | Issue | ISSN |
312 | 10 | 0012-365X |
Citations | PageRank | References |
0 | 0.34 | 3 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Lisa Berger | 1 | 0 | 0.34 |
| Moshe Dror | 2 | 574 | 64.77 |
| James Lynch | 3 | 0 | 0.34 |