Formulas
| Any f | Injective f | Surjective f | |
|---|---|---|---|
| Distinct | |||
| Sn orbits | |||
| Sx orbits | |||
| Sn×Sx orbits |
Formulas for the different cases of the twelvefold way are summarized in the table on the right; each table entry links to a subsection below explaining the formula. The particular notations used are the following:
- the falling factorial power ,
- the factorial
- the Stirling number of the second kind, denoting the number of ways to partition a set of n elements into k subsets
- the binomial coefficient
- the Iverson bracket encoding a truth value as 0 or 1
- the number of partitions of n into k parts
Read more about this topic: Twelvefold Way
Famous quotes containing the word formulas:
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—Jerome S. Bruner (20th century)
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—Hermann Hesse (1877–1962)
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—John Dos Passos (1896–1970)