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Signature

  • 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 1.8.13, Section 3.2.5Section 3.7.11.
  • See also: Order, Sort, Cross, Minors, Det.
  • Related package: DiscreteMath`Combinatorica`.

    Further Examples

    The first list is in canonical order. The second needs three transpositions to put it in canonical order.

    In[1]:=

    Out[1]=

    In[2]:=

    Out[2]=