Permutation Lexicographic Unrank
Unrank a zero-based lexicographic index permutation from exact integer text and an explicit bounded size.
Description
Unrank a zero-based lexicographic index permutation from exact integer text and an explicit bounded size.
A zero-based lexicographic rank identifies one permutation among size factorial arrangements.
When to use this tool
Unrank a zero-based lexicographic index permutation from exact integer text and an explicit bounded size.
- Prepare the supplied size, rank 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 size, rank. 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.permutation. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.
Require size from 0 to 128 and decimal rank in [0, size!). Decode factorial-weighted Lehmer digits and select each digit-th remaining index.1
| Input field | Meaning and representation | Accepted input |
|---|---|---|
| size | size. | Safe integer |
| rank | Exact decimal integer text; keep it quoted in JSON rather than converting through a floating-point number. | Optional leading + or - and 1 to 256 decimal digits; no whitespace |
| Output field | Interpretation |
|---|---|
| result | Object containing the named outputs below. |
| result.permutation | The permutation list in the ordering and representation described above. |
{
"input": {
"size": 3,
"rank": "4"
},
"output": {
"result": {
"permutation": [
2,
0,
1
]
}
}
}Limitations and assumptions
- The empty permutation has one rank, zero. The rank convention is lexicographic and not an arbitrary numeric encoding.
- 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
- Permutation Lexicographic Rank
Return a zero-based exact lexicographic permutation rank as decimal integer text; no floating factorial approximation.
- Next Lexicographic Permutation
Return the next lexicographic index permutation without wraparound; null marks the boundary of the permutation order.