Definition:Permutation/Ordered Selection/Notation

Definition

The number of $r$-permutations from a set of cardinality $n$ is denoted variously:

${}_n P_r$

${P_n}^r$

$p_{n r}$

${}^n P_r$

There is little consistency in the literature.

On $\mathsf{Pr} \infty \mathsf{fWiki}$ the notation of choice is ${}^n P_r$.

Sources

• 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text I$. Algebra: Permutations and Combinations
• 1964: A.M. Yaglom and I.M. Yaglom: Challenging Mathematical Problems With Elementary Solutions: Volume $\text { I }$ ... (previous) ... (next): Problems
• 1971: George E. Andrews: Number Theory ... (previous) ... (next): $\text {3-1}$ Permutations and Combinations: Theorem $\text {3-1}$
• 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.5$: Permutations and Factorials
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): permutation