6.9.10  Signature of a permutation: signature

Every permutation can be decomposed into a product of transpositions (cycles with only two elements). The number of transpositions is not unique, but for any permutation the number will be either odd or even. The signature of a permutation is equal to:

• 1 if the permutation is equal to an even product of transpositions,
• -1 if the permutation is equal to an odd product of transpositions.

The signature of a cycle of size k is: (−1)^k+1.

The signature command computes the signature of a permutation.

• signature takes one argument:
  p, a permutation.
• signature(p) returns the signature of the permutation p.

Example.
Input:

Output: