Determines whether a substitution is even or odd. (3 characters)
Author: shiroeExecutions: 119
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A permutation that can be expressed as the product of an even number of transpositions is an even permutation,
while a permutation that can be expressed as the product of an odd number of transpositions is an odd permutation.
For an even permutation, the parity check returns "even" and outputs 1.
If it is an odd permutation, the parity is set to odd, and -1 is output.
The parity of a permutation is sometimes used in the definition of a determinant.
Enter the result of permuting 123 in the input field.
In permutation notation, this is often written in the bottom row.
For example, if you want to check the parity of 132—which is the result of permuting 123—
set Input 1 to 1, Input 2 to 3, and Input 3 to 2.
The program will output the parity result.
Enter any of the digits 1, 2, or 3 for inputs 1, 2, and 3.
Ensure that the inputs for 1, 2, and 3 are all different and contain no duplicates.
while a permutation that can be expressed as the product of an odd number of transpositions is an odd permutation.
For an even permutation, the parity check returns "even" and outputs 1.
If it is an odd permutation, the parity is set to odd, and -1 is output.
The parity of a permutation is sometimes used in the definition of a determinant.
Enter the result of permuting 123 in the input field.
In permutation notation, this is often written in the bottom row.
For example, if you want to check the parity of 132—which is the result of permuting 123—
set Input 1 to 1, Input 2 to 3, and Input 3 to 2.
The program will output the parity result.
Enter any of the digits 1, 2, or 3 for inputs 1, 2, and 3.
Ensure that the inputs for 1, 2, and 3 are all different and contain no duplicates.
| Sequence of numbers | |
| Even/Odd Determination | (Even = 1, Odd = -1) |
R6 (2024). 03/27 (Wed)_Ver.substitution_n=3, i=1,2,3
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Here, we consider the permutation of the number sequence 123.
This determines whether a 3-character permutation σ is even or odd.
If even, sgn(σ) = 1;
if odd, sgn(σ) = -1;
and
outputs 1 or -1 as the result.