Description
Return one conjugate-partition column height.
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 one conjugate-partition column height.
When to use this tool
Use Partition Conjugate Single Column Height when checking the stated partition, permutation or rotation/reflection convention.
How to use the tool and how it works
- Enter partition, column. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read height. Use the output convention below.
Return one conjugate-partition column height. Require a nonincreasing positive integer partition and column >= 1; height counts parts at least that column.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| partition | Partition | Required. Array of safe integer; maximum items 256. |
| column | Column | Required. Safe integer; minimum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| height | Height | Required. Safe integer. |
{
"input": {
"partition": [
4,
2,
1
],
"column": 2
},
"output": {
"height": 2
}
}Limitations and assumptions
- Columns are one-based; empty or beyond-width columns return zero rather than generating the full conjugate diagram.
- 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
- Combinatorics: Partition Ferrers Cell Count
Return Ferrers diagram cell, row and column counts.
- Set Partition Block Insertion Weight
Return insertion choices for a set partition with a supplied block count.