File:Inversion example; Rothe and invset 1.svg

Rothe diagram and place-based inversion set of ${\displaystyle {\begin{pmatrix}1&2&3&4&5&6\\2&5&4&6&3&1\end{pmatrix}}}$

Right inversion vector r and inversion vector v are calculated with the help of a Rothe diagram.
The left inversion vector l is shown as the vector of row sums of the inversion set triangle.
${\displaystyle l(i)=v(\pi (i))}$, therefore ${\displaystyle l}$ can also be seen in ${\displaystyle v}$ below the Rothe diagram by using the blue inverse permutation on top as index.
E.g. ${\displaystyle l(3)=v(\pi (3))=v(4)=1}$. Or graphically: To find ${\displaystyle l(3)}$, go down from the blue 3 to find the red 1.

v:Inversion (discrete mathematics)

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