Euler's Partition Function Theory Finished

universegeek writes "Mathematician Ken Ono, from Emory, has solved a 250-year-old problem: how to exactly and explicitly generate partition numbers. Ono and colleagues were able to finally do this by realizing that the pattern of partition numbers is fractal (PDF). This pattern allowed them to find a finite, algebraic formula, which is like striking oil in mathematics."

Comments

Re:In English

[martin-boundary]

Suppose you have a large amount of data, and you've turned it into a whole lot of integers. You might not want to store the integers each in a full byte/word/double word, as you'd be wasting a lot of memory that way.

So you come up with a scheme where small integers are stored in a slot that only takes up the number of bits that they actually need. For example, the number 5 can be stored in 3 bits or more, and the number 3 can be stored in two bits or more, which is a far cry from the "standard" size of 64 bits per integer used on many computers these days.

The Euler partition function tells you in how many ways you can split 64 bits up into differently sized slots, which is great if you want to design flexible encoding schemes that make good use of those 64 bits.