Description
Compose two supplied permutation parity flags.
Combinatorial checks often evaluate necessary conditions or one algebraic component. Parity can be combined from supplied signs, a divisibility test can constrain an orbit size, and prefix sums can enforce a strict positivity condition. Passing one condition does not construct or prove the existence of the full combinatorial object.
Compose two supplied permutation parity flags.
When to use this tool
Use Permutation Inversion Parity Compose when you already have firstOdd, secondOdd and need to compose two supplied permutation parity flags.
How to use the tool and how it works
- Enter firstOdd, secondOdd. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read compositionOdd. Inspect compositionOdd before interpreting the associated values.
Return firstOdd!==secondOdd as compositionOdd.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| firstOdd | First Odd | Required. Boolean. |
| secondOdd | Second Odd | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| compositionOdd | Exclusive OR of supplied parity flags; no permutations or inversion counts are inspected. | Required. Boolean. |
{
"input": {
"firstOdd": true,
"secondOdd": true
},
"output": {
"compositionOdd": false
}
}Limitations and assumptions
- This combines supplied signs, not permutations. No permutation, inversion count, composition order or input validity is checked.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
Alternative or Complementary methods
Use a complete construction, enumeration or proof for the mathematical question. Keep integer ranges, empty-input conventions and strict inequalities explicit when incorporating these local checks into a larger algorithm.
References
Similar or alternative tools
- Orbit Size Divisibility Remainder
Check divisibility of a group order by a proposed orbit size.
- Binomial Coefficient Symmetry Index
Calculate symmetric and smaller binomial-coefficient indices.