Description
Check whether a proposed period divides a word length.
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.
Check whether a proposed period divides a word length.
When to use this tool
Use Necklace Period Divisor Flag when checking the stated partition, permutation or rotation/reflection convention.
How to use the tool and how it works
- Enter length, proposedPeriod. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read divides, repetitions. Inspect divides before interpreting the associated values.
Check whether a proposed period divides a word length. Require whole length >= 1 and period in [1,length]; divides tests zero remainder, repetitions = floor(length/period).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| length | Length | Required. Safe integer; minimum 1. |
| proposedPeriod | Proposed Period | Required. Safe integer; minimum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| divides | Divides | Required. Boolean. |
| repetitions | floor(length/proposedPeriod); not an exact repetition count when divides=false. | Required. Safe integer. |
{
"input": {
"length": 12,
"proposedPeriod": 3
},
"output": {
"divides": true,
"repetitions": 4
}
}Limitations and assumptions
- When divides is false the quotient is truncated, not a valid repetition count; no word content or minimal period is inspected.
- 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 Rotation Fixed Position Count
Return position cycles induced by a rotation.
- Necklace Orbit Size
Return a bead word's rotation orbit and stabilizer sizes.