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Results tagged with partitions
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user 21724
3
votes
Sum involving integer compositions and binomial coefficients
Here are three reasons for this to be false :
When $k=1, n=2, a_1=1, b_1=0$ I get $(j+1)(j+2)$ on the LHS and $j+1 + \binom{3+j}{3}$ on the RHS.
The (ordinary) generating function of the LHS (with r …
- 7,249
7
votes
Accepted
Particular sum on product partitions into k parts
If you only need an upper bound of the right order of magnitude, I strongly recommend the use of Rankin's trick, which amounts to write
$$
\sum_{r \leq R} f(r) \leq \prod_{p \leq R} \left( \sum_{\ell …
- 7,249