Simple alternative to the Hardy-Ramanujan-Rademacher formula for p(N)

dc.creatorChase, N. M.
dc.date2004-04-22
dc.date.accessioned2026-07-07T04:31:07Z
dc.date.available2026-07-07T04:31:07Z
dc.descriptionA 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.description25 pages, submitted to The Electronic Journal of Combinatorics
dc.identifierhttps://arxiv.org/abs/math-ph/0404050
dc.identifierhttp://arxiv.org/abs/math-ph/0404050
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57705
dc.subjectMathematical Physics
dc.subject05A17; 11P81
dc.titleSimple alternative to the Hardy-Ramanujan-Rademacher formula for p(N)
dc.typetext

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