Description
Assign each labeled insertion independently to one of N+1 original sequence gaps uniformly; repeated gaps permitted, not uniform over count compositions.
A random construction is defined by its sampling support: positions, permutations, complete tilings, proposal sequences or another explicit set. Uniform choices at one stage do not necessarily make final visible outcomes uniform. A replay seed gives a deterministic sequence; equal values can hide different sampled positions. These tools are for reproducible synthetic examples rather than cryptographic entropy.
Assign each labeled insertion independently to one of N+1 original sequence gaps uniformly; repeated gaps permitted, not uniform over count compositions.
When to use this tool
Use this tool to assign each labeled insertion independently to one of N+1 original sequence gaps uniformly; repeated gaps permitted, not uniform over count compositions.
How to use the tool and how it works
- Enter length, insertions, seed using the definitions below.
- Run the operation. Resolve input-format errors before interpreting an output.
- Read result.seed, result.gaps, result.counts, using the stated boundary, ordering, sign and absence conventions.
For a source length 0–127, draw each insertion gap independently from 0…length. Return the gap for every insertion and a count for each of length+1 gaps.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| length | Explicit integer source/sequence length under the bounds stated above. | Finite safe integer satisfying the stated bounds. |
| insertions | Number of independent labeled insertions, integer 1–128. | Finite safe integer satisfying the stated bounds. |
| seed | Nonblank replay seed, at most 256 UTF-16 code units; an injected source overrides seeded draws. | Text, at most 8,192 UTF-16 code units; narrower grammar/range rules also apply. |
| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.seed | Original supplied seed string; injected-source replay additionally requires that source’s state. |
| result.gaps | One sampled zero-based insertion gap per labeled insertion. |
| result.counts | Number of insertions allocated to every original gap. |
{
"input": {
"length": 3,
"insertions": 2,
"seed": "batch56"
},
"output": {
"result": {
"seed": "batch56",
"gaps": [
2,
3
],
"counts": [
0,
0,
1,
1
]
}
}
}Limitations and assumptions
- insertions is 1–128. Assignments of labeled insertions are uniform, whereas aggregate gap-count vectors are not uniformly distributed.
- A nonblank seed of at most 256 UTF-16 code units is required. With ordinary use the seed initializes one deterministic advancing source; an application-injected random source takes precedence and the seed alone then cannot replay the result. Uniformity statements assume independent uniform source draws in [0,1). Source calls are bounded and degenerate injected sources can fail a rejection budget. This is not cryptographically secure.
- Every declared outer field is required and unknown outer fields are rejected. Strings and JSON text have size limits, lists are bounded to 128 entries, and JSON nesting/node counts are bounded. Tighter operation-specific bounds stated above take precedence.
- Ordinary numeric outputs must be finite and within safe-integer magnitude. Exact large lengths/counts use decimal strings. Original record indexes and code-unit positions are zero-based; span ends are exclusive unless stated otherwise.
Alternative or Complementary methods
Choose a generator whose support matches the intended experiment and retain source-position provenance. Use a separate statistically justified process model or cryptographic source where those properties matter.
References
Similar or alternative tools
- Random Block Order Permutation
Uniform whole-block position permutation preserving internal order and duplicate display labels.
- Random Bounded Chunk Cut Positions
Uniformly sample bounded positive chunk-length compositions of an explicit total with fixed chunk count using exact completion-count unranking; infeasible support rejects.