Construction of Permutations/Proof 2/Example

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 $3$
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