PermutationLength
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PermutationLength
Details

- PermutationLength works with Cycles objects as well as with permutation lists.
- The number of integers moved by a permutation is sometimes called its degree. Another common definition of permutation degree is the largest moved point.
Examples
open allclose allBasic Examples (2)Summary of the most common use cases
Scope (2)Survey of the scope of standard use cases
Number of integers in the support of a permutation in cyclic form:

https://wolfram.com/xid/0g7gmi119ju-b5qmz8

Length of the support of the identity:

https://wolfram.com/xid/0g7gmi119ju-d93mts

Number of integers in the support of a permutation list:

https://wolfram.com/xid/0g7gmi119ju-i7pmxd

Length of the support of the identity permutation list:

https://wolfram.com/xid/0g7gmi119ju-wxxg58

Generalizations & Extensions (1)Generalized and extended use cases
The length of the support of a permutation group is defined as the length of the union of the supports of its elements:

https://wolfram.com/xid/0g7gmi119ju-86cqti

Support length of the default permutation representation of a named abstract group:

https://wolfram.com/xid/0g7gmi119ju-p825q5

Properties & Relations (1)Properties of the function, and connections to other functions
PermutationLength is equivalent to using Length on the permutation support:

https://wolfram.com/xid/0g7gmi119ju-7rrrra

Wolfram Research (2010), PermutationLength, Wolfram Language function, https://reference.wolfram.com/language/ref/PermutationLength.html.
Text
Wolfram Research (2010), PermutationLength, Wolfram Language function, https://reference.wolfram.com/language/ref/PermutationLength.html.
Wolfram Research (2010), PermutationLength, Wolfram Language function, https://reference.wolfram.com/language/ref/PermutationLength.html.
CMS
Wolfram Language. 2010. "PermutationLength." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/PermutationLength.html.
Wolfram Language. 2010. "PermutationLength." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/PermutationLength.html.
APA
Wolfram Language. (2010). PermutationLength. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PermutationLength.html
Wolfram Language. (2010). PermutationLength. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PermutationLength.html
BibTeX
@misc{reference.wolfram_2025_permutationlength, author="Wolfram Research", title="{PermutationLength}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/PermutationLength.html}", note=[Accessed: 16-May-2025
]}
BibLaTeX
@online{reference.wolfram_2025_permutationlength, organization={Wolfram Research}, title={PermutationLength}, year={2010}, url={https://reference.wolfram.com/language/ref/PermutationLength.html}, note=[Accessed: 16-May-2025
]}