Unformatted text preview: α ∈ S n and τ is a transposition, and we let β = τσ , then the di ﬀ erence of the number of inversions of α and β is odd. This can be seen via a case distinction. If τ = ( ij ) , then any constellation between a triple i , j , k can only change either from 0 inversions in α to 3 inversions in β , 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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This note was uploaded on 10/13/2010 for the course MATH 435 at Penn State.