Construction of Permutations/Proof 2/Example
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Example of Construction of Permutations
From the permutation of $4$ objects $3 1 2 4$, the following permutations of $5$ objects can be made as follows:
- $3 1 2 4 \dfrac 1 2$
- $3 1 2 4 \dfrac 3 2$
- $3 1 2 4 \dfrac 5 2$
- $3 1 2 4 \dfrac 7 2$
- $3 1 2 4 \dfrac 9 2$
Renaming according to size:
- $4 2 3 5 1$
- $4 1 3 5 2$
- $4 1 2 5 3$
- $3 1 2 5 4$
- $3 1 2 4 5$
Sources
- 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.5$: Permutations and Factorials: Exercise $3$