Simple alternative to the Hardy-Ramanujan-Rademacher formula for p(N)
| dc.creator | Chase, N. M. | |
| dc.date | 2004-04-22 | |
| dc.date.accessioned | 2026-07-07T04:31:07Z | |
| dc.date.available | 2026-07-07T04:31:07Z | |
| dc.description | A recent paper examined the global structure of integer partitions sequences and, via combinatorial analysis using modular arithmetic, derived a closed form expression for a map from (N, M) to the set of all partitions of a positive integer N into exactly M positive integer summands. The output of the IPS map was a "matrix" having M columns and a number of rows equal to p[N, M], the number of partitions of N into M parts. The global structure of integer partition sequences (IPS) is that of a complex tree. In this paper, we examine the structure of the IPS tree and, by counting the number of directed paths through the tree, obtain a simple formula which gives, in closed form, the total number of partitions of N into exactly M parts. By summing over M, we obtain a transparent alternative to the Hardy-Ramanujan-Rademacher formula for p(N). | |
| dc.description | 25 pages, submitted to The Electronic Journal of Combinatorics | |
| dc.identifier | https://arxiv.org/abs/math-ph/0404050 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0404050 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/57705 | |
| dc.subject | Mathematical Physics | |
| dc.subject | 05A17; 11P81 | |
| dc.title | Simple alternative to the Hardy-Ramanujan-Rademacher formula for p(N) | |
| dc.type | text |