Identifier
Identifier
Values
[1] => 1
[1,2] => 1
[2,1] => -1
[1,2,3] => 1
[1,3,2] => -1
[2,1,3] => -1
[2,3,1] => 1
[3,1,2] => 1
[3,2,1] => -1
[1,2,3,4] => 1
[1,2,4,3] => -1
[1,3,2,4] => -1
[1,3,4,2] => 1
[1,4,2,3] => 1
[1,4,3,2] => -1
[2,1,3,4] => -1
[2,1,4,3] => 1
[2,3,1,4] => 1
[2,3,4,1] => -1
[2,4,1,3] => -1
[2,4,3,1] => 1
[3,1,2,4] => 1
[3,1,4,2] => -1
[3,2,1,4] => -1
[3,2,4,1] => 1
[3,4,1,2] => 1
[3,4,2,1] => -1
[4,1,2,3] => -1
[4,1,3,2] => 1
[4,2,1,3] => 1
[4,2,3,1] => -1
[4,3,1,2] => -1
[4,3,2,1] => 1
[1,2,3,4,5] => 1
[1,2,3,5,4] => -1
[1,2,4,3,5] => -1
[1,2,4,5,3] => 1
[1,2,5,3,4] => 1
[1,2,5,4,3] => -1
[1,3,2,4,5] => -1
[1,3,2,5,4] => 1
[1,3,4,2,5] => 1
[1,3,4,5,2] => -1
[1,3,5,2,4] => -1
[1,3,5,4,2] => 1
[1,4,2,3,5] => 1
[1,4,2,5,3] => -1
[1,4,3,2,5] => -1
[1,4,3,5,2] => 1
[1,4,5,2,3] => 1
[1,4,5,3,2] => -1
[1,5,2,3,4] => -1
[1,5,2,4,3] => 1
[1,5,3,2,4] => 1
[1,5,3,4,2] => -1
[1,5,4,2,3] => -1
[1,5,4,3,2] => 1
[2,1,3,4,5] => -1
[2,1,3,5,4] => 1
[2,1,4,3,5] => 1
[2,1,4,5,3] => -1
[2,1,5,3,4] => -1
[2,1,5,4,3] => 1
[2,3,1,4,5] => 1
[2,3,1,5,4] => -1
[2,3,4,1,5] => -1
[2,3,4,5,1] => 1
[2,3,5,1,4] => 1
[2,3,5,4,1] => -1
[2,4,1,3,5] => -1
[2,4,1,5,3] => 1
[2,4,3,1,5] => 1
[2,4,3,5,1] => -1
[2,4,5,1,3] => -1
[2,4,5,3,1] => 1
[2,5,1,3,4] => 1
[2,5,1,4,3] => -1
[2,5,3,1,4] => -1
[2,5,3,4,1] => 1
[2,5,4,1,3] => 1
[2,5,4,3,1] => -1
[3,1,2,4,5] => 1
[3,1,2,5,4] => -1
[3,1,4,2,5] => -1
[3,1,4,5,2] => 1
[3,1,5,2,4] => 1
[3,1,5,4,2] => -1
[3,2,1,4,5] => -1
[3,2,1,5,4] => 1
[3,2,4,1,5] => 1
[3,2,4,5,1] => -1
[3,2,5,1,4] => -1
[3,2,5,4,1] => 1
[3,4,1,2,5] => 1
[3,4,1,5,2] => -1
[3,4,2,1,5] => -1
[3,4,2,5,1] => 1
[3,4,5,1,2] => 1
[3,4,5,2,1] => -1
[3,5,1,2,4] => -1
[3,5,1,4,2] => 1
[3,5,2,1,4] => 1
[3,5,2,4,1] => -1
[3,5,4,1,2] => -1
[3,5,4,2,1] => 1
[4,1,2,3,5] => -1
[4,1,2,5,3] => 1
[4,1,3,2,5] => 1
[4,1,3,5,2] => -1
[4,1,5,2,3] => -1
[4,1,5,3,2] => 1
[4,2,1,3,5] => 1
[4,2,1,5,3] => -1
[4,2,3,1,5] => -1
[4,2,3,5,1] => 1
[4,2,5,1,3] => 1
[4,2,5,3,1] => -1
[4,3,1,2,5] => -1
[4,3,1,5,2] => 1
[4,3,2,1,5] => 1
[4,3,2,5,1] => -1
[4,3,5,1,2] => -1
[4,3,5,2,1] => 1
[4,5,1,2,3] => 1
[4,5,1,3,2] => -1
[4,5,2,1,3] => -1
[4,5,2,3,1] => 1
[4,5,3,1,2] => 1
[4,5,3,2,1] => -1
[5,1,2,3,4] => 1
[5,1,2,4,3] => -1
[5,1,3,2,4] => -1
[5,1,3,4,2] => 1
[5,1,4,2,3] => 1
[5,1,4,3,2] => -1
[5,2,1,3,4] => -1
[5,2,1,4,3] => 1
[5,2,3,1,4] => 1
[5,2,3,4,1] => -1
[5,2,4,1,3] => -1
[5,2,4,3,1] => 1
[5,3,1,2,4] => 1
[5,3,1,4,2] => -1
[5,3,2,1,4] => -1
[5,3,2,4,1] => 1
[5,3,4,1,2] => 1
[5,3,4,2,1] => -1
[5,4,1,2,3] => -1
[5,4,1,3,2] => 1
[5,4,2,1,3] => 1
[5,4,2,3,1] => -1
[5,4,3,1,2] => -1
[5,4,3,2,1] => 1
click to show generating function       
Description
The sign of a permutation.
References
[1] Section 1.3 Stanley, R. P. Enumerative combinatorics. Volume 1 MathSciNet:2868112
Code
def statistic(x):
    return x.sign()
   
Created
Feb 14, 2013 at 04:32 by Sara Billey
Updated
Jun 01, 2015 at 17:56 by Martin Rubey