toqito.perms.perm_sign

toqito.perms.perm_sign(perm)

Compute the “sign” of a permutation [WikParPerm].

The sign (either -1 or 1) of the permutation perm is -1**`inv, where inv is the number of inversions contained in perm.

Examples

For the following vector

\[[1, 2, 3, 4]\]

the permutation sign is positive as the number of elements in the vector are even. This can be performed in toqito as follows.

>>> from toqito.perms import perm_sign
>>> perm_sign([1, 2, 3, 4])
1

For the following vector

\[[1, 2, 3, 4, 5]\]

the permutation sign is negative as the number of elements in the vector are odd. This can be performed in toqito as follows.

>>> from toqito.perms import perm_sign
>>> perm_sign([1, 2, 4, 3, 5])
-1

References

[WikParPerm]

Wikipedia: Parity of a permutation https://en.wikipedia.org/wiki/Parity_of_a_permutation

Parameters:

perm – The permutation vector to be checked.

Returns:

The value 1 if the permutation is of even length and the value of -1 if the permutation is of odd length.