All Questions
Tagged with integer-partitions analytic-number-theory
3
questions
3
votes
1
answer
169
views
How to extend Euler's identity regarding partition on the unit disk?
Theorem (Euler) $:$ For $|x|<1$ we have
$$\prod\limits_{m=1}^{\infty} \frac {1} {1-x^m} = \sum\limits_{n=0}^{\infty} p(n) x^n,$$ where $p(n)$ denotes the number of partitions of $n$ for $...
- 2,013
1
vote
1
answer
235
views
Number of unordered factorizations of a non-square-free positive integer
I recently discovered that the number of multiplicative partitions of some integer $n$ with $i$ prime factors is given by the Bell number $B_i$, provided that $n$ is a square-free integer. So, is ...
- 1,611
0
votes
0
answers
53
views
Clarification of the proof of Euler's identity regarding the generating function for partitions.
In reference to this question which I asked here couple of days back but didn't get any answer I am posting this question to clarify whether we can able to extend Euler's identity regarding the ...
- 2,013