Description
Insert a zero into a weak composition.
Combinatorial counts depend on whether objects are labeled, order matters, repetitions are permitted and a prefix is already fixed. Local counts, exact integer factors and feasibility bounds answer specific questions and need not enumerate complete objects.
Insert a zero into a weak composition.
When to use this tool
Use Integer Composition Zero Part Insertion when checking the stated word, set, multiset or composition convention.
How to use the tool and how it works
- Enter parts, position. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read parts. Use the output convention below.
Insert a zero into a weak composition. Require nonnegative whole parts with length < 256 and position in [0,length]; return the prefix, one zero and the suffix as a new array.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| parts | Parts | Required. Array of safe integer; maximum items 256. |
| position | Position | Required. Safe integer; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| parts | Parts | Required. Array of safe integer; maximum items 256. |
{
"input": {
"parts": [
2,
3
],
"position": 1
},
"output": {
"parts": [
2,
0,
3
]
}
}Limitations and assumptions
- Insertion preserves total but changes slot count; no distinct-composition count or position equivalence is calculated.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use complete objects and an appropriate exact counting, ranking or enumeration method when the local contribution is insufficient.
References
Similar or alternative tools
- Composition Zero Part Capacity
Return zero-part count and remaining allowed capacity.
- Cyclic Composition Part Count
Count positive compositions up to cyclic rotation.