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Mathematics-Online lexicon:

Transpositions, Sign of a Permutation


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A transposition

$\displaystyle \tau = (j,k)
$

is an exchange of $ j$ and $ k$. By composition of these elementary permutations, any permutation $ \pi$ can be represented by:

$\displaystyle \pi = \tau_1 \circ \cdots \circ \tau_m\, ,
$

where the parity (even or odd $ m$) is uniquely determined. Thus, the so called sign of permutation $ \pi$ is well defined by

$\displaystyle \sigma(\pi) = (-1)^m\, .
$

(Authors: Burkhardt/Höllig/Knesch)

Annotation:


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  automatically generated 3/31/2005