Combination Colexicographic Unrank
Exact zero-based colexicographic combination unranking on bounded sorted distinct indexes; results are integer text or explicit index witnesses.
Description
Exact zero-based colexicographic combination unranking on bounded sorted distinct indexes; results are integer text or explicit index witnesses.
Colexicographic combination order prioritizes the largest differing selected index. Its rank convention differs from ordinary lexicographic order.
When to use this tool
Exact zero-based colexicographic combination unranking on bounded sorted distinct indexes; results are integer text or explicit index witnesses.
- Prepare the supplied size, count, 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, count, 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.indexes. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.
Validate size, count and zero-based rank below choose(size,count). For j descending from count, choose the largest x below the current limit with choose(x,j) no greater than rank, subtract that term and continue. Return increasing indexes.1
| Input field | Meaning and representation | Accepted input |
|---|---|---|
| size | size. | Integer from 0 to 128 inclusive |
| count | count. | Integer from 0 to size inclusive |
| 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.indexes | The indexes list in the ordering and representation described above. |
{
"input": {
"size": 4,
"count": 2,
"rank": "1"
},
"output": {
"result": {
"indexes": [
0,
2
]
}
}
}Limitations and assumptions
- Ranks use exact decimal strings and universes are at most 128. The tool does not accept a rank from another ordering convention.
- 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
Retain the universe size, subset size and ordering convention with a rank. Use rank/unrank pairs from the same convention and distinguish subset masks from lexicographic indexes.
References
Similar or alternative tools
- Combination Colexicographic Rank
Exact zero-based colexicographic combination ranking on bounded sorted distinct indexes; results are integer text or explicit index witnesses.
- Combination Lexicographic Unrank
Exact zero-based lexicographic combination unranking on bounded sorted distinct indexes; results are integer text or explicit index witnesses.