# PermutationListQ

PermutationListQ[expr]

returns True if expr is a valid permutation list and False otherwise.

# Details

• A valid permutation list {p1,,pn} is a rearrangement of the integers {1,,n}.

# Examples

open allclose all

## Basic Examples(1)

A valid permutation list:

Invalid permutation lists:

## Scope(2)

PermutationListQ works efficiently with large permutation lists:

The empty list is considered a permutation list of length and degree 0:

## Properties & Relations(4)

RandomSample[Range[n]] always gives a valid permutation list:

A possible, but less efficient, Wolfram Language implementation:

Validity of permutations in cyclic form is checked with PermutationCyclesQ. A permutation list can always be obtained as a permutation of the elements in canonical order using Permute:

Ordering always returns a permutation list, even if the elements of the expression are repeated:

## Neat Examples(1)

There are 409113 integer numbers up to whose decimal digits form permutation lists. This is how the first 153 (the largest being 54321) are distributed:

Wolfram Research (2010), PermutationListQ, Wolfram Language function, https://reference.wolfram.com/language/ref/PermutationListQ.html.

#### Text

Wolfram Research (2010), PermutationListQ, Wolfram Language function, https://reference.wolfram.com/language/ref/PermutationListQ.html.

#### CMS

Wolfram Language. 2010. "PermutationListQ." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/PermutationListQ.html.

#### APA

Wolfram Language. (2010). PermutationListQ. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PermutationListQ.html

#### BibTeX

@misc{reference.wolfram_2024_permutationlistq, author="Wolfram Research", title="{PermutationListQ}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/PermutationListQ.html}", note=[Accessed: 18-September-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_permutationlistq, organization={Wolfram Research}, title={PermutationListQ}, year={2010}, url={https://reference.wolfram.com/language/ref/PermutationListQ.html}, note=[Accessed: 18-September-2024 ]}