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**Unformatted text preview: **S n and is a transposition, and we let = , then the di erence of the number of inversions of and is odd. This can be seen via a case distinction. If = ( ij ) , then any constellation between a triple i , j , k can only change either from 0 inversions in to 3 inversions in , or from 1 to 2 inversions, or 2 to 1 inversion, or 3 to 0 inversions. This gives an overall count of odd....

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