All Questions
4
questions
1
vote
1
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288
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A certain conjectured criterion for restricted partitions
Given the number of partitions of $n$ into distinct parts $q(n)$, with the following generating function
$\displaystyle\prod_{m=1}^\infty (1+x^m) = \sum_{n=0}^\infty q(n)\,x^n\tag{1a}$
Which may be ...
- 2,813
3
votes
0
answers
333
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Unsolved problems for partition function
In number theory, the partition function $p(n)$ represents the number of possible partitions of a non-negative integer $n$. For instance, $p(4) = 5$ because the integer $4$ has the five partitions $1 +...
- 907
3
votes
0
answers
71
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Are there exist infinitely many odd numbers and even numbers in p(an+b)?
The main question is: Are there exist infinitely many odd numbers and even numbers in $p(an+b)$? Where $an+b\ (n\geq1)$ is an arbitrary arithmetic sequence with $a\in\mathbb{Z}_{>0}$, $b\in\{0,\...
- 907
4
votes
2
answers
1k
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Learning about partitions and modular forms
I'm interested in learning about partitions and modular forms. I already know algebra and analysis (complex and real). Can any one suggest me books or other materials from where I can learn these ...
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