Article
A Formula for the Partition Function That "Counts"
Annals of Combinatorics
Document Type
Article
Publication Date
6-1-2016
DOI
10.1007/s00026-016-0305-1
Disciplines
- Education and
- Mathematics
Abstract
We derive a combinatorial multisum expression for the number D(n, k) of partitions of n with Durfee square of order k. An immediate corollary is therefore a combinatorial formula for p(n), the number of partitions of n. We then study D(n, k) as a quasipolynomial. We consider the natural polynomial approximation D~(n,k) to the quasipolynomial representation of D(n, k). Numerically, the sum ∑1≤k≤√n D~(n, k) appears to be extremely close to the initial term of the Hardy-Ramanujan-Rademacher convergent series for p(n).
Citation Information
Yuriy Choliy and Andrew V. Sills. "A Formula for the Partition Function That "Counts"" Annals of Combinatorics Vol. 20 Iss. 2 (2016) p. 301 - 316 ISSN: 0219-3094 Available at: http://works.bepress.com/andrew_sills/56/