Determines whether a substitution is even or odd. (4 characters)
Author: shiroeExecutions: 165
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Enter the result of substituting 1234 (the sequence of numbers for which you want to check even/odd) into the input field.
In substitution notation, this is often written in the bottom row.
For example, if you want to check whether the sequence 1324—which is the result of replacing 1234 (by swapping the order)—is even or odd,
set Input 1 to 1, Input 2 to 3, Input 3 to 2, and Input 4 to 4.
The calculator will output the result of the even/odd check.
Enter any of the digits 1, 2, 3, or 4 into Input 1, 2, 3, and 4.
Enter distinct digits (no duplicates) into Input 1, 2, 3, and 4.
In substitution notation, this is often written in the bottom row.
For example, if you want to check whether the sequence 1324—which is the result of replacing 1234 (by swapping the order)—is even or odd,
set Input 1 to 1, Input 2 to 3, Input 3 to 2, and Input 4 to 4.
The calculator will output the result of the even/odd check.
Enter any of the digits 1, 2, 3, or 4 into Input 1, 2, 3, and 4.
Enter distinct digits (no duplicates) into Input 1, 2, 3, and 4.
| Entered sequence of numbers | (A sequence of numbers substituting for 1234) |
| Even/Odd Determination | (Even = 1, Odd = -1) |
R6 (2024). 04/09 (Tue) _Even/Odd Determination by Substitution. 4 characters. _001
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Here, we consider the permutation of the number sequence 1234.
This determines whether a 4-character permutation σ is even or odd.
If the permutation is even, sgn(σ) = 1;
if it is odd, sgn(σ) = -1.
The program outputs 1 or -1 as the result.
A permutation that can be expressed as the product of an even number of transpositions is an even permutation;
a permutation that can be expressed as the product of an odd number of transpositions is an odd permutation.
If the permutation is even, the parity is determined to be even, and 1 is output.
If the permutation is odd, the parity is determined to be odd, and -1 is output.
Determining the parity of a permutation is sometimes used in the definition of determinants.