Combination Colexicographic Rank
Exact zero-based colexicographic combination ranking on bounded sorted distinct indexes; results are integer text or explicit index witnesses.
Description
Exact zero-based colexicographic combination ranking on bounded sorted distinct indexes; results are integer text or explicit index witnesses.
A combination's colex rank is a sum of binomial coefficients based on its increasing indexes.
When to use this tool
Exact zero-based colexicographic combination ranking on bounded sorted distinct indexes; results are integer text or explicit index witnesses.
- Prepare the supplied indexes, 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 indexes, 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.rank. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.
Validate indexes inside size and compute the exact sum of choose(index[j], j plus one), returning decimal text.1
| Input field | Meaning and representation | Accepted input |
|---|---|---|
| indexes | indexes. | List of finite numbers; at most 128 entries |
| size | size. | Safe integer |
| Output field | Interpretation |
|---|---|
| result | Object containing the named outputs below. |
| result.rank | The rank value under the stated formula or text convention. |
{
"input": {
"indexes": [
0,
2
],
"size": 4
},
"output": {
"result": {
"rank": "1"
}
}
}Limitations and assumptions
- This zero-based rank differs from lexicographic rank. Input order must be strictly increasing and duplicates are invalid.
- 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.