Description
Extend a rotation orbit by a supplied reflection-symmetry flag.
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.
Extend a rotation orbit by a supplied reflection-symmetry flag.
When to use this tool
Use Circular Arrangement Reflection Orbit Size when checking the stated partition, permutation or rotation/reflection convention.
How to use the tool and how it works
- Enter rotations, reflectionSymmetric. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read orbit. Use the output convention below.
Extend a rotation orbit by a supplied reflection-symmetry flag. Require bounded positive whole rotations; orbit = rotations when reflectionSymmetric, otherwise twice rotations.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| rotations | Rotations | Required. Safe integer; minimum 1; maximum 1000000. |
| reflectionSymmetric | Reflection Symmetric | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| orbit | Orbit | Required. Safe integer. |
{
"input": {
"rotations": 5,
"reflectionSymmetric": false
},
"output": {
"orbit": 10
}
}Limitations and assumptions
- The rotation-orbit size and reflection symmetry are asserted, not established from a circular word or group action.
- 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
- Necklace Orbit Size
Return a bead word's rotation orbit and stabilizer sizes.
- Circular Permutation Anchor Factor
Return the supplied rotation-anchor factor.