A Formula for the Partition Function That "Counts"

作者：Choliy Yuriy^*; Sills Andrew V

来源：Annals of Combinatorics, 2016, 20(2): 301-316.

DOI：10.1007/s00026-016-0305-1

• integer partitions
• partition function
• Durfee square

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) over tilde (n, k) to the quasipolynomial representation of D(n, k). Numerically, the sum Sigma(1 <= k <=root n (D) over tilde)(n, k) appears to be extremely close to the initial term of the Hardy-Ramanujan-Rademacher convergent series for p(n).

• 出版日期2016-6
• 单位rutgers