Description
Return sign and parity of a transposition count.
Partitions, permutations and circular words use distinct encodings and symmetry conventions. Parity, block bounds and orbit-size identities can follow from supplied counts without verifying a complete object or identifying its actual symmetry.
Return sign and parity of a transposition count.
When to use this tool
Use Permutation Transposition Count Parity when checking the stated partition, permutation or rotation/reflection convention.
How to use the tool and how it works
- Enter count. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read sign, even. Inspect even before interpreting the associated values.
Return sign and parity of a transposition count. Require a valid whole count; sign is -1 for odd and +1 for even, and even reports modulo-two equality.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| count | Whole transposition count; parity is interpreted modulo two. | Required. Safe integer; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| sign | Sign | Required. Safe integer. |
| even | Even | Required. Boolean. |
{
"input": {
"count": 3
},
"output": {
"sign": -1,
"even": false
}
}Limitations and assumptions
- This uses a supplied count rather than verifying a permutation or a transposition decomposition.
- 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.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Validate the complete combinatorial object and its action/labeling convention before applying whole-object enumeration, ranking or symmetry conclusions.
References
Similar or alternative tools
- Combinatorics: Permutation Cycle Parity From Count
Return permutation sign from size and cycle count.
- Permutation Prefix Forced Fixed Count
Count forced fixed points in a permutation prefix.