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PermutationLength
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PermutationLength

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returns the number of integers moved by the permutation perm.

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 all

Basic Examples  (2)Summary of the most common use cases

Number of points moved by a permutation:

In[1]:=1
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https://wolfram.com/xid/0g7gmi119ju-nbaysm
Out[1]=1

Number of points moved in a permutation list:

In[1]:=1
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https://wolfram.com/xid/0g7gmi119ju-ptr9lx
Out[1]=1

Scope  (2)Survey of the scope of standard use cases

Number of integers in the support of a permutation in cyclic form:

In[1]:=1
✖
https://wolfram.com/xid/0g7gmi119ju-b5qmz8
Out[1]=1

Length of the support of the identity:

In[2]:=2
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https://wolfram.com/xid/0g7gmi119ju-d93mts
Out[2]=2

Number of integers in the support of a permutation list:

In[1]:=1
✖
https://wolfram.com/xid/0g7gmi119ju-i7pmxd
Out[1]=1

Length of the support of the identity permutation list:

In[2]:=2
✖
https://wolfram.com/xid/0g7gmi119ju-wxxg58
Out[2]=2

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:

In[1]:=1
✖
https://wolfram.com/xid/0g7gmi119ju-86cqti
Out[1]=1

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

In[2]:=2
✖
https://wolfram.com/xid/0g7gmi119ju-p825q5
Out[2]=2

Properties & Relations  (1)Properties of the function, and connections to other functions

PermutationLength is equivalent to using Length on the permutation support:

In[1]:=1
✖
https://wolfram.com/xid/0g7gmi119ju-7rrrra
Out[1]=1
Wolfram Research (2010), PermutationLength, Wolfram Language function, https://reference.wolfram.com/language/ref/PermutationLength.html.
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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.

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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.

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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

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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 ]}

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@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 ]}

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@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 ]}