Signature[list] gives the signature of the permutation needed to place the elements of list in canonical order.
Examples: Signature[a,b,c] ; Signature[a,c,b] .
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[list] gives 0.
See The Mathematica Book: Section 1.8.15, Section 3.2.5 and Section 3.7.11.
See also: Order, Sort, Cross, Minors, Det, KroneckerDelta.
Related package: DiscreteMath`Combinatorica`.