A Formula for the Partition Function That "Counts"
Document Type
Article
Publication Date
6-2016
Publication Title
Annals of Combinatorics
DOI
10.1007/s00026-016-0305-1
ISSN
0219-3094
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).
Recommended Citation
Choliy, Yuriy, Andrew V. Sills.
2016.
"A Formula for the Partition Function That "Counts"."
Annals of Combinatorics, 20 (2): 301-316.
doi: 10.1007/s00026-016-0305-1
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/359
