- general overview: [1]
- The "Twelvefold way":
[1]
[2]
[3]
balls per urn: unrestricted ≤1 ≥1 *n*labelled balls,*m*labelled urns*n*-tuples

of*m*things*n*-permutations

of*m*thingspartitions of {1, ... , n}

into ≤*m*ordered parts*n*unlabelled balls,*m*labelled urns*n*-multicombinations

of*m*things*n*-multicombinations

of*m*things*n*-combinations

of*m*things*n*labelled balls,*m*unlabelled urnspartitions of {1, ... , n}

into ≤*m*parts*n*pigeons

in*m*holespartitions of {1, ... , n}

into*m*parts*n*unlabelled balls,*m*unlabelled urnspartitions of *n*

into ≤*m*parts*n*pigeons

in*m*holespartitions of *n*

into*m*parts - "balls and urns" is sometimes modeled as "stars and bars" [2]

__Knuth's "The Art of Computer Programming"__

- 7.2. Generating All Possibilities
- 7.2.1. Generating Basic Combinatorial Patterns
- 7.2.1.1. Generating all n-tuples
- 7.2.1.2. Generating all permutations
- 7.2.1.3. Generating all combinations
- 7.2.1.4. Generating all partitions
- 7.2.1.5. Generating all set partitions
- 7.2.1.6. Generating all trees
- 7.2.1.7. History and further references