] gives the signature of the permutation needed to place the elements of list in canonical order.
The signature of the permutation is , where is the number of transpositions of pairs of elements that must be composed to build up the permutation.
If any two elements of list are the same, Signature[
] gives 0.
See the Mathematica book: Section 1.8.13, Section 3.2.5, Section 3.7.11.
See also: Order, Sort, Cross, Minors, Det.
Related package: DiscreteMath`Combinatorica`.
The first list is in canonical order. The second needs three transpositions to put it in canonical order.
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