Permutation Cycle Notation Parser
Parse zero-based disjoint cycle notation on an explicit index universe; overlapping cycles are rejected instead of interpreted as cycle products.
Description
Parse zero-based disjoint cycle notation on an explicit index universe; overlapping cycles are rejected instead of interpreted as cycle products.
Disjoint cycle notation can reconstruct an index permutation when its total size is supplied. Omitted indexes remain fixed.
When to use this tool
Parse zero-based disjoint cycle notation on an explicit index universe; overlapping cycles are rejected instead of interpreted as cycle products.
- Prepare the supplied notation, size 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 notation, size. 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.
Accept whitespace-separated decimal indexes inside parenthesized cycles, including empty cycles. Require every used index in range and used at most once. Start with identity and map each cycle entry to its successor, wrapping to the first.1
| Input field | Meaning and representation | Accepted input |
|---|---|---|
| notation | notation. | Text; at most 8,192 UTF-16 code units, subject to the grammar above |
| size | size. | Integer from 0 to 128 inclusive |
| Output field | Interpretation |
|---|---|
| result | Object containing the named outputs below. |
| result.permutation | The permutation list in the ordering and representation described above. |
{
"input": {
"notation": "(0 2 1)(3)",
"size": 4
},
"output": {
"result": {
"permutation": [
2,
0,
1,
3
]
}
}
}Limitations and assumptions
- Products of overlapping cycles are rejected rather than composed. The syntax does not accept commas or symbolic labels.
- 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 Cycle Notation Formatter
Format canonical zero-based disjoint permutation cycles with an explicit fixed-point display policy; no one-based convention implied.
- Index Permutation Cycle Table
Decompose an index permutation into disjoint cycles, including fixed points and starting each cycle at its smallest unseen index.