Partition Function

An integer $n$ can be written as a sum of different positive integers. Its also called partitions of an integer or $P(n)$.

For $4$, there are $5$ partitions.

$4 = 3+1 = 2+2 = 2+1+1 = 1+1+1+1$

So $P(4) = 5$.

Partitions were studied by many mathematicians like Euler, Ramanujam, Hardy and also by Freeman Dyson. But the finite formula for partitions was discovered by Dr. Ken Ono and Jane Bruinier at Emory University. You can plug in any number in that formula and get the partitions for it.

I first came to know about partitions when I watched this beautiful video by Dr. Ken Ono.

2 months ago we were assigned to give a presentation on some specific topics in physics.

Even though the topics I got were from statistical mechanics, I included the mathematical partition function also.

The slides can be seen here – Partition Functions by Shivani Mishra

I have not shared the remaining 20 slides which contain derivations of statistical partition functions and other statistical mechanics definitions.