Basic Examples 
(2)
 

Here is the inversion vector of a permutation:
In[28]:=
iv=ResourceFunction["ToInversionVector"]@{3,5,4,1,2}
Out[28]=
{3,3,0,1,0}
This gives back the permutation:
In[30]:=
[◼]
FromInversionVector
@iv
Out[30]=
{3,5,4,1,2}

Scope 
(3)
 
