Description
Count forced fixed points in a permutation prefix.
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.
Count forced fixed points in a permutation prefix.
When to use this tool
Use Permutation Prefix Forced Fixed Count when checking the stated partition, permutation or rotation/reflection convention.
How to use the tool and how it works
- Enter prefixValues, totalSize, origin. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read fixedInPrefix, remainingPositions. Use the output convention below.
Count forced fixed points in a permutation prefix. Require origin zero/one, nonnegative whole totalSize, unique in-range prefix values and prefix length <= total; fixedInPrefix counts value === index+origin, remainingPositions = total-prefix length.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| prefixValues | Prefix Values | Required. Array of safe integer; maximum items 256. |
| totalSize | Total Size | Required. Safe integer; minimum 0. |
| origin | Origin | Required. Safe integer. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| fixedInPrefix | Fixed In Prefix | Required. Safe integer. |
| remainingPositions | Remaining Positions | Required. Safe integer. |
{
"input": {
"prefixValues": [
1,
3,
2
],
"totalSize": 5,
"origin": 1
},
"output": {
"fixedInPrefix": 1,
"remainingPositions": 2
}
}Limitations and assumptions
- This does not count fixed points in the unknown suffix or enumerate valid completions.
- 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
- Permutation Transposition Count Parity
Return sign and parity of a transposition count.
- Permutation Fixed Point Free Budget
Check whether a requested fixed-point count leaves a possible derangement size.