Permutation Lehmer Code
Encode a validated index permutation as a Lehmer inversion code with one digit per original position.
Description
Encode a validated index permutation as a Lehmer inversion code with one digit per original position.
Lehmer coding records how many smaller indexes follow each entry of a permutation.
When to use this tool
Encode a validated index permutation as a Lehmer inversion code with one digit per original position.
- Prepare the supplied permutation fields for this operation.
- Compare the complete example with the representation used by your own input before carrying the result into another step.
How to use the tool and how it works
- Enter permutation. Use the exact text syntax, units and index conventions explained below.
- Run the tool. If input validation fails, correct the supplied fields before interpreting any result.
- Read result.digits. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.
Validate the index permutation and, at each position, count later values smaller than the current value. Return the digit list in source order.1
| Input field | Meaning and representation | Accepted input |
|---|---|---|
| permutation | permutation. | List of finite numbers; at most 128 entries |
| Output field | Interpretation |
|---|---|
| result | Object containing the named outputs below. |
| result.digits | The digits list in the ordering and representation described above. |
{
"input": {
"permutation": [
2,
0,
1
]
},
"output": {
"result": {
"digits": [
2,
0,
0
]
}
}
}Limitations and assumptions
- Digits encode the declared zero-based value ordering. They are not the permutation inverse or cycle lengths.
- Except in the diagnostic validator, a permutation must contain each integer from zero through length minus one exactly once. Lists contain at most 128 entries.
- All declared input fields are required and unexpected top-level fields are rejected. Numbers must be finite; lists are limited to 128 entries and ordinary text fields to 8,192 UTF-16 code units, with tighter limits where stated.
- JSON text inputs must parse within bounded nesting and size limits. Numeric outputs outside the safe finite range are rejected; large exact integer results use decimal strings. Indexes and half-open spans are zero-based unless a rank is explicitly described as one-based.
Alternative or Complementary methods
Keep the index-to-image convention and composition direction explicit. A rank, cycle table, reorder-index list and inverse map encode different operations even when their entries are all integers.
References
Similar or alternative tools
- Lehmer Code Permutation Decoder
Decode a bounded Lehmer code by selecting each digit from the remaining sorted index universe; invalid digit ranges are rejected.
- Index Permutation Composition
Compose index permutations by applying first then second to each index; composition convention is explicit and operand lengths must agree.