Description
Assign unique supplied right-bank IDs to left-bank IDs by a uniform full bijection, not arbitrary graph matching or schedule generation.
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 unique supplied right-bank IDs to left-bank IDs by a uniform full bijection, not arbitrary graph matching or schedule generation.
When to use this tool
Use this tool to assign unique supplied right-bank IDs to left-bank IDs by a uniform full bijection, not arbitrary graph matching or schedule generation.
How to use the tool and how it works
- Enter left, right, seed using the definitions below.
- Run the operation. Resolve input-format errors before interpreting an output.
- Read result.seed, result.pairs, using the stated boundary, ordering, sign and absence conventions.
Require equally sized distinct-ID banks with at least two entries. Fisher–Yates shuffle the right bank and pair its results with the fixed left-bank order.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| left | Distinct literal left-bank IDs in fixed pairing order. | Dense list of at most 128 literal strings, each at most 8,192 UTF-16 units. |
| right | Distinct literal right-bank IDs, or the nonnegative right-move count for a grid route. | Dense list of at most 128 literal strings, each at most 8,192 UTF-16 units. |
| 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.pairs | Generated bank matches or per-pair orientation records with original provenance. |
{
"input": {
"left": [
"a",
"b"
],
"right": [
"x",
"y"
],
"seed": "batch56"
},
"output": {
"result": {
"seed": "batch56",
"pairs": [
{
"left": "a",
"right": "x"
},
{
"left": "b",
"right": "y"
}
]
}
}
}Limitations and assumptions
- The sample space is bijections between the two labeled banks, rather than arbitrary unordered pairs or matching under constraints.
- 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 Two-Level Run Trace
Choose a fair initial level and independent uniform run lengths, then alternate two explicit distinct levels; support is level/run assignments, not uniform over all bounded traces.
- Random Two-Row Domino Tiling
Uniformly sample complete domino tilings of a 2xN board via exact Fibonacci completion counts and rank unranking, reporting vertical singles or paired horizontal domino placements.