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$\begin{CD} A @>a>> B \\ @VVbV @VVcV \\ C @>d>> D \end{CD}$

Second column is incomplete, but sorting works (by specifying keys). Disregard behavior of rows with empty second column. Discuss here or at Mathematician talk:Mathematicians/Sorted By Nation. --barto (talk) 15:31, 16 July 2017 (EDT)

Indexed Summation does not Change under Permutation

Surgery
Let $\sigma = \begin{bmatrix} k & k+1 \end{bmatrix}$ be an adjacent transposition in $S_n$, with $1\leq k \leq n-1$.

We have: