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Results tagged with partitions
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user 32332
12
votes
Accepted
Generating function of $p(25n + 24)$
Hirschhorn and Hunt have published a note M. D. Hirschhorn; D. C. Hunt, A simple proof of the Ramanujan conjecture for powers of 5, J. Reine Angew. Math., 326 (1981), 1-17., where they give a proof (w …
- 12.1k
2
votes
Accepted
What is the relationship between Partition function and Betti numbers for nilpotent Lie alge...
There are formulas for the Betti numbers of $\mathfrak{f}_n$ in terms of restricted partitions. …
- 12.1k
16
votes
Partitions-sum of divisors identity
2.) There is a proof, due to P. Erdös, in the Annals of Mathematics (2), 43, 1942, pp. 437-450, which does not use the generating function, but rather proves the identity
$$
np(n)=\sum_{m=1}^n \sum_{k …
- 12.1k