Mathematics-Online lexicon: Transpositions, Sign of a Permutation

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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

and

. 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

) is uniquely determined. Thus, the so called sign of permutation $\pi$ is well defined by

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

(Authors: Burkhardt/Höllig/Knesch)

Examples:

automatically generated 3/31/2005