Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Given two positive numbers $r,s$, what is a positive solution of $$\sum_{i=0}^{m-1} k_i = r \quad\text{ and } \quad \sum_{i=0}^{m-1} (i+1)k_i = s \quad ??$$

I would like to get some reference to treat this kind of partition.

remark: There is a famous related subject called "Ewens's sampling formula".

share|cite|improve this question

This is a partition of $s$ into $r$ non-zero parts, with $k_i$ parts $i+1$. It would seem slightly more straightforward to write it as

$$ \sum_{i=1}^mk_i=r\quad\text{and}\quad\sum_{i=1}^mik_i=s $$

with $k_i$ parts $i$.

share|cite|improve this answer
This is so far from an answer. I don't understand why the people are voting up. It is nothing more than an opinion about how to write a problem, without a solution, answer or hint. – Lewis S. Feb 2 '13 at 14:54
@Lewis: Then I think you need to state your question more specifically. It seemed to me from the question that you weren't aware that this is a partition of $s$ into $r$ non-zero parts. Since you can find loads of information on that by googling once you know what it's called, I was under the impression that I had given you the main information that you'd been lacking. If that's not the case, I suggest that you edit the question to reflect more specifically what it is you want to know about these partitions. – joriki Feb 2 '13 at 16:25

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.