Partitions of a Number

Question

Given a natural number n, how do we find the recurrence for the number of distinct partitions of the number? Note: 4 -> {4},{3,1},{2,2},{1,1,1,1},{2,1,1} Here, {1,3} and {3,1} are the considered the same Also, can we get a closed form for the recurrence?

Thanks!

Here's a relevant recurrence (though probably not everything you were looking for): http://math.stackexchange.com/questions/1908701/ — David K, Nov 02 '16 at 18:10

Mathily · Answer 1 · 2016-11-02T20:49:48.297

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The Online Encyclopedia of Integer Sequences is a great place to look for this sort of thing.

There are explicit functions, like Rademacher's formula which can be truncated to give very accurate asymptotics. There are also many recurrence relations, all of which you can find an overview of on Wolfram Mathworld.

In both cases the link will take you to the entry on the 'partition function', which is the name of what you are asking about.

edited Nov 02 '16 at 20:49

answered Nov 02 '16 at 18:31

Mathily

528

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There is no known explicit formula? There is Rademacher's exact formula and more, see here. – Dietrich Burde Nov 02 '16 at 20:16
@DietrichBurde Thanks for the link, the Folsom-Masri paper from that link gives a nice exposition about exact formulae. – Mathily Nov 02 '16 at 20:46
Yes, this is a nice paper! – Dietrich Burde Nov 02 '16 at 20:58

Partitions of a Number

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