Definition:Permutation on n Letters/Set of Permutations
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Definition
Let $\N_k$ be used to denote the (one-based) initial segment of natural numbers:
- $\N_k = \closedint 1 k = \set {1, 2, 3, \ldots, k}$
The set of permutations of $\N_n$ is denoted $S_n$.
Also denoted as
Some sources use $\map S n$ for $S_n$.
Also see
Sources
- 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 3.6$. Products of bijective mappings. Permutations: Example $54$
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text I$: Algebraic Structures: $\S 7$: Semigroups and Groups: Example $7.5$
- 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $2$: Examples of Group Structure: $\S 30$
- 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 34$. Examples of groups: $(4) \ \text {(c)}$
- 1996: John F. Humphreys: A Course in Group Theory ... (previous) ... (next): Chapter $9$: Permutations