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Function Repository Resource:

 PermutationSkewSum

Source Notebook

Compute the skew sum of permutation lists

Contributed by: Motoharu Ito

ResourceFunction["PermutationSkewSum"][perm1,perm2,…]

gives the skew sum of the permutations permi.

Details

The skew sum of two permutations p=p1,p2,…,pm and q=q1,q2,…,qn is .

Examples

Basic Examples (2) 

The skew sum of {1,4,3,2,5} and {4,2,3,1}:

In[1]:=
ResourceFunction["PermutationSkewSum"][{1, 4, 3, 2, 5}, {4, 2, 3, 1}]
Out[1]=

The skew sum of four permutations:

In[2]:=
ResourceFunction[ "PermutationSkewSum"][{2, 1}, {1, 3, 2}, {1, 2, 4, 3}, {1, 2, 3, 5, 4}]
Out[2]=

Properties and Relations (2) 

The skew sum is not commutative:

In[3]:=
ResourceFunction["PermutationSkewSum"][{1, 4, 3, 2, 5}, {4, 2, 3, 1}]
Out[3]=
In[4]:=
ResourceFunction["PermutationSkewSum"][{4, 2, 3, 1}, {1, 4, 3, 2, 5}]
Out[4]=

The skew sum is associative:

In[5]:=
ResourceFunction["PermutationSkewSum"][ ResourceFunction[ "PermutationSkewSum"][{1, 4, 3, 2, 5}, {1, 3, 2}], {4, 2, 3, 1}]
Out[5]=
In[6]:=
ResourceFunction["PermutationSkewSum"][{1, 4, 3, 2, 5}, ResourceFunction["PermutationSkewSum"][{1, 3, 2}, {4, 2, 3, 1}]]
Out[6]=

Publisher

Motoharu Ito

Version History

  • 1.0.0 – 29 November 2022

Source Metadata

  • Citation:
    Kitaev S., Patterns in Permutations and Words. Springer, 2013.

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