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≤nD~(n,k) appears to be extremely close to the initial term of the Hardy-Ramanujan-Rademacher convergent series for p(n).
Original language | American English |
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Journal | Annals of Combinatorics |
Volume | 20 |
DOIs | |
State | Published - Jun 1 2016 |
Keywords
- Durfee square
- Integer partitions
- Partition function
DC Disciplines
- Education
- Mathematics