Description
Return an integer partition's Durfee-square size.
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 an integer partition's Durfee-square size.
When to use this tool
Use Combinatorics: Integer Partition Durfee Size when checking the stated partition, permutation or rotation/reflection convention.
How to use the tool and how it works
- Enter parts. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read result. Expand result to inspect the returned fields.
Return an integer partition's Durfee-square size. Require positive nonincreasing whole parts; count indexes j with parts[j] >= j+1.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| parts | Parts | Required. Array of finite number. Implementation limit: 128 items. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Returned calculated value or nested object under the stated output convention. | Required. Object. |
| result.durfeeSize | Durfee Size | Calculated result member: number. |
{
"input": {
"parts": [
4,
3,
1
]
},
"output": {
"result": {
"durfeeSize": 2
}
}
}Limitations and assumptions
- Empty partition gives zero; this checks the supplied Ferrers shape rather than generating or counting partitions.
- Outputs are nested inside result. 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
- Partition Conjugate Single Column Height
Return one conjugate-partition column height.
- Combinatorics: Partition Ferrers Cell Count
Return Ferrers diagram cell, row and column counts.