The Sign of a Permutation
نویسنده
چکیده
This is not the only way to write (abc) using transpositions, e.g., (abc) = (bc)(ac) = (ac)(ab). Since any permutation in Sn is a product of cycles and any cycle is a product of transpositions, any permutation in Sn is a product of transpositions. 1 Unlike the unique decomposition of a permutation into a product of disjoint cycles, the decomposition of a permutation as a product of transpositions is almost never into disjoint transpositions: there will usually be overlaps in the numbers moved by different transpositions.
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