# Direct sum of permutations

In combinatorial mathematics, the direct sum of the permutation π of length m and the permutation σ of length n is the permutation of length m + n defined by

$(\pi\oplus\sigma)(i) = \begin{cases} \pi(i) & \text{for }1\le i\le m,\\ \sigma(i-m)+m & \text{for }m+1\le i\le m+n.\end{cases}$

• Skew sum of permutations

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