Basic Examples (2)
Basic Examples
(2)
This permutation has three numbers greater than 1 before 1, two numbers greater than 2 before 2 and so on:
In[609]:=
{4,3,2,1};
Therefore this is its inversion vector:
In[610]:=
{3,2,1,0};
Here is a check:
In[6]:=
Out[6]=
True
———
The positive integer 23 gives in the factorial base, so is an inversion vector:
{3,2,1,0}
{3,2,1,0}
In[9]:=
IntegerDigits[23,MixedRadix[{4,3,2,1}]]
Out[9]=
{3,2,1,0}
Every inversion vector must end in 0 because the largest entry in a permutation list has nothing but smaller entries before it:
In[5]:=
Out[5]=
False