M-partitions: Optimal partitions of weight for one scale pan
| dc.creator | O'Shea, Edwin | |
| dc.date | 2003-11-14 | |
| dc.date.accessioned | 2026-07-07T05:02:53Z | |
| dc.date.available | 2026-07-07T05:02:53Z | |
| dc.description | An M-partition of a positive integer m is a partition with as few parts as possible such that any positive integer less than m has a partition made up of parts taken from that partition of m. This is equivalent to partitioning a weight m so as to be able to weigh any integer weight l < m with as few weights as possible and only one scale pan. We show that the number of parts of an M-partition is a log-linear function of m and the M-partitions of m correspond to lattice points in a polytope. We exhibit a recurrence relation for counting the number of M-partitions of m and, for ``half'' of the positive integers, this recurrence relation will have a generating function. The generating function will be, in some sense, the same as the generating function for counting the number of distinct binary partitions for a given integer. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/math/0311230 | |
| dc.identifier | http://arxiv.org/abs/math/0311230 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69187 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A17 | |
| dc.title | M-partitions: Optimal partitions of weight for one scale pan | |
| dc.type | text |