All Questions
5
questions
7
votes
2
answers
126
views
A sum of partitions
A friend of mine presented a problem I found interesting:
Compute the following: $$\sum_{n=0}^\infty\left(\prod_{k=1}^j(1+x^k)\right)[x^{mn}]$$ where $P(x)[x^n]$ denotes the $x^n$ coefficient of $P$...
2
votes
3
answers
2k
views
Algorithm for the number of partitions of $n$ into distinct parts
I am looking for an algorithm to find the number of ways of writing $n$ as a sum of positive integers without regard to order with the constraint that all integers in a given partition are distinct. ...
- 65
1
vote
1
answer
49
views
How we can partition $a_1, a_2, a_3, ... a_n$ in two sequence X and Y such that their sum of differences be minimum?
I couldn't write any algorithm that can do this in good order for $a_i < 100$ and $n < 2000$ :(
how we can partition $a_1, a_2, a_3, ... a_n$ in two sequence X and Y such that $|X_1 - X_2| + |...
1
vote
1
answer
55
views
What is the name of the transform which finds the number of ways to make partitions of the given sizes?
I'm looking for the name of a transform which takes a sequence giving the number of 'prime' elements of a given size to the number of ways to make a number out of a sum of 'prime' elements, up to ...
- 32.3k
0
votes
1
answer
119
views
General term of this sequence
I wanted to know the General term or the function to generate this sequence I found on OEIS.
It is the number of ways to express $2n+1$ as $p+2q$; where $p$ and $q$ can be odd prime number and even ...
- 827