In combinatorics, a Stirling number of the second kind (or Stirling partition number) is the number of ways to partition a set of n objects into k non-empty subsets and is denoted by S(n,k)1. This online calculator calculates the Stirling number of the second kind for the given n, for each k from 0 to n and outputs results into a table. Note that this calculator uses the "big integers" library (see Tips and tricks #9: Big numbers), so you can try pretty big n values.
For example, the number of ways to partition a set of 100 objects into 28 non-empty subsets is 77697 3005359874 5155212806 6127875847 8739787812 8370115840 9749925701 0238608628 9805848025 0748224048 4354517896 0761551674. A combinatorial explosion, that is :)
For those who curious, the explicit formula is listed below the calculator.
Stirling numbers formula
Ronald L. Graham, Donald E. Knuth, Oren Patashnik (1988) Concrete Mathematics, Addison–Wesley, Reading MA. ISBN 0-201-14236-8, p. 244. ↩
- • Combinatorics. Permutation generator from N to M with repetitions.
- • Stirling's approximation of factorial
- • Combinatorics. Permutation generator from n to m without repetitions
- • Combinatorics – combinations, arrangements and permutations
- • Making up words out of the syllables
- • Combinatorics section ( 26 calculators )