Wolfram Function Repository
Instant-use add-on functions for the Wolfram Language
Function Repository Resource:
Compute the permutation graph of a permutation
ResourceFunction["PermutationGraph"][p] gives the permutation graph for the permutation p. |
GraphComplement gives the permutation graph of the reverse permutation p:
In[2]:= | ![]() |
Out[2]= | ![]() |
In[3]:= | ![]() |
Out[3]= | ![]() |
In[4]:= | ![]() |
Out[4]= | ![]() |
In[5]:= | ![]() |
Out[5]= | ![]() |
The number of inversions in a permutation can be computed by the resource function InvesionCount and is equal to the number of edges in its permutation graph:
In[6]:= | ![]() |
Out[6]= | ![]() |
In[7]:= | ![]() |
Out[7]= | ![]() |
Every clique in a permutation graph corresponds to a decreasing sequence in the corresponding permutation:
In[8]:= | ![]() |
Out[8]= | ![]() |
In[9]:= | ![]() |
In[10]:= | ![]() |
Out[10]= | ![]() |
A maximum-size clique corresponds to one of the longest decreasing sequences:
In[11]:= | ![]() |
Out[11]= | ![]() |
In[12]:= | ![]() |
Out[12]= | ![]() |
This work is licensed under a Creative Commons Attribution 4.0 International License