Description
Return inversion-count change for swapping adjacent supplied values.
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 inversion-count change for swapping adjacent supplied values.
When to use this tool
Use Permutation Adjacent Swap Inversion Delta when checking the stated partition, permutation or rotation/reflection convention.
How to use the tool and how it works
- Enter left, right. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read delta. Use the output convention below.
Return inversion-count change for swapping adjacent supplied values. delta is +1 when left < right, -1 when left > right and zero when equal.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| left | Left | Required. Finite number. |
| right | Right | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| delta | Delta | Required. Safe integer. |
{
"input": {
"left": 2,
"right": 5
},
"output": {
"delta": 1
}
}Limitations and assumptions
- This assumes only those adjacent entries exchange positions; no complete inversion count or valid permutation 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.
- 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 Cycle Split Sign
Return relative sign from a supplied cycle-count change.