Arrangements

Ordered selections of $k$ distinct elements from $\{1, …, n\}$ — the $k$ -permutations of $n$ .

Arrangements(n, k)Ordered selections of

k

distinct elements from

\{1, …, n\}

— the

k

-permutations of

n

Typed signatures

Type	Package	Applies
`(integer<0..>, integer<0..>) -> indexed_collection<arrangement>`	`combinatorics`	always

Domain: Collections

Details

Count is the falling factorial $n^{\underline{k}} = n!/(n-k)!$ .
Each element is a length- $k$ one-line word with distinct entries from $\{1, …, n\}$ .

Examples

1 more kept as data, checked against the oracles

Basic #

$Count(Arrangements(4, 2)) = 12$

\mathrm{Count}(\mathrm{Arrangements}(4, 2))

Out

12

The first element in enumeration order

\mathrm{Arrangements}(4, 2)[1]

Out

{\operatorname{Arrangement}}([1, 2])

About

Examples	3
Crosswalk	OEIS ×2 Wolfram Language SageMath SymPy mathlib4