Description
Return the supplied rotation-anchor factor.
Partitions, permutations and circular words use distinct encodings and symmetry conventions. Parity, block bounds and orbit-size identities can follow from supplied counts without verifying a complete object or identifying its actual symmetry.
Return the supplied rotation-anchor factor.
When to use this tool
Use Circular Permutation Anchor Factor when checking the stated partition, permutation or rotation/reflection convention.
How to use the tool and how it works
- Enter items, labeledRotation. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read factor. Use the output convention below.
Return the supplied rotation-anchor factor. Require whole items >= 1; factor = items when labeledRotation, otherwise one.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| items | Items | Required. Safe integer; minimum 1. |
| labeledRotation | Labeled Rotation | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| factor | Multiplier in the direction defined above; not automatically a complete converted quantity. | Required. Safe integer. |
{
"input": {
"items": 5,
"labeledRotation": true
},
"output": {
"factor": 5
}
}Limitations and assumptions
- This is a convention-dependent multiplier, not the number of circular arrangements or a verified symmetry/stabilizer factor.
- 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
Validate the complete combinatorial object and its action/labeling convention before applying whole-object enumeration, ranking or symmetry conclusions.
References
Similar or alternative tools
- Circular Arrangement Reflection Orbit Size
Extend a rotation orbit by a supplied reflection-symmetry flag.
- Necklace Orbit Size
Return a bead word's rotation orbit and stabilizer sizes.