All Questions
4
questions
4
votes
1
answer
430
views
How To Apply and Understand the Generating Function for Number Partitioning
The function p(n) counts the number of ways a number can be made up of smaller numbers. For example, the p(5) = 7 because you ...
7
votes
1
answer
233
views
What is the significance of this identity relating to partitions?
I was watching a talk given by Prof. Richard Kenyon of Brown University, and I was confused by an equation briefly displayed at the bottom of one slide at 15:05 in the video.
$$1 + x + x^3 + x^6 + \...
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0
votes
0
answers
94
views
Truncation of partitions generating function question
$A (x)$ is the generating function for partitions. $B(x)=\sum_{n=0}^{\infty}b_nx^n $
$$b_n =\binom{\text{number of partitions of }n}{\text{into an even number of parts}}-\binom{\text{number of ...
- 1,725
2
votes
1
answer
943
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Proof that the series for the generating function of the partition function converges?
For $|q| < 1$, the generating function of the partition function $p(n)$ is given by
$$
\sum_{n=0}^\infty p(n) q^n
= \prod_{k=1}^\infty {1 \over 1-q^k}. \tag{1}
$$
I have an intuitive ...
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