Combination Lexicographic Unrank
Exact zero-based lexicographic combination unranking on bounded sorted distinct indexes; results are integer text or explicit index witnesses.
Description
Exact zero-based lexicographic combination unranking on bounded sorted distinct indexes; results are integer text or explicit index witnesses.
Lexicographic unranking selects a combination by counting how many earlier choices each possible next index would skip.
When to use this tool
Exact zero-based lexicographic 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.
Require size at most 128, count within size and decimal rank below choose(size,count). At each position subtract binomial completion-block sizes until locating the containing block, then choose that index.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
- The rank is zero-based and specific to lexicographic order. No full combination list is constructed.
- 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 Unrank
Exact zero-based colexicographic combination unranking on bounded sorted distinct indexes; results are integer text or explicit index witnesses.
- Combination Lexicographic Rank
Exact zero-based lexicographic combination ranking on bounded sorted distinct indexes; results are integer text or explicit index witnesses.