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PermutationMin
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PermutationMin

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returns the smallest integer moved by the permutation perm.

Examples

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

Smallest point moved by a permutation:

In[1]:=1
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https://wolfram.com/xid/0puxjt0rmu-gdlvcy
Out[1]=1

Smallest point moved in a permutation list:

In[1]:=1
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https://wolfram.com/xid/0puxjt0rmu-fwfj0
Out[1]=1

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

Smallest integer of the support of a permutation in cyclic form:

In[1]:=1
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https://wolfram.com/xid/0puxjt0rmu-b5qmz8
Out[1]=1

Minimum of the support of the identity:

In[2]:=2
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https://wolfram.com/xid/0puxjt0rmu-d93mts
Out[2]=2

Smallest integer of the support of a permutation list:

In[1]:=1
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https://wolfram.com/xid/0puxjt0rmu-dybbmq
Out[1]=1

Minimum of the support of the identity permutation list:

In[2]:=2
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https://wolfram.com/xid/0puxjt0rmu-wxxg58
Out[2]=2

Generalizations & Extensions  (1)Generalized and extended use cases

Smallest integer moved by the elements of a permutation group:

In[1]:=1
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https://wolfram.com/xid/0puxjt0rmu-86cqti
Out[1]=1

Smallest integer moved by the default permutation representation of a named abstract group:

In[2]:=2
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https://wolfram.com/xid/0puxjt0rmu-p825q5
Out[2]=2

Properties & Relations  (2)Properties of the function, and connections to other functions

On Cycles objects, PermutationMin is equivalent to applying Min:

In[1]:=1
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https://wolfram.com/xid/0puxjt0rmu-hrlo74
Out[1]=1

On both Cycles objects and permutation lists, PermutationMin is equivalent to using Min on the permutation support:

In[1]:=1
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https://wolfram.com/xid/0puxjt0rmu-4zyahb
Out[1]=1
Wolfram Research (2010), PermutationMin, Wolfram Language function, https://reference.wolfram.com/language/ref/PermutationMin.html.
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Wolfram Research (2010), PermutationMin, Wolfram Language function, https://reference.wolfram.com/language/ref/PermutationMin.html.

Text

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

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

CMS

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

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

APA

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

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

BibTeX

@misc{reference.wolfram_2025_permutationmin, author="Wolfram Research", title="{PermutationMin}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/PermutationMin.html}", note=[Accessed: 05-May-2025 ]}

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@misc{reference.wolfram_2025_permutationmin, author="Wolfram Research", title="{PermutationMin}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/PermutationMin.html}", note=[Accessed: 05-May-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_permutationmin, organization={Wolfram Research}, title={PermutationMin}, year={2010}, url={https://reference.wolfram.com/language/ref/PermutationMin.html}, note=[Accessed: 05-May-2025 ]}

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@online{reference.wolfram_2025_permutationmin, organization={Wolfram Research}, title={PermutationMin}, year={2010}, url={https://reference.wolfram.com/language/ref/PermutationMin.html}, note=[Accessed: 05-May-2025 ]}