Description
Return insertion choices for a set partition with a supplied block count.
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 insertion choices for a set partition with a supplied block count.
When to use this tool
Use Set Partition Block Insertion Weight when checking the stated partition, permutation or rotation/reflection convention.
How to use the tool and how it works
- Enter blocks. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read existingBlockChoices, newBlockChoices, totalChoices. Use the output convention below.
Return insertion choices for a set partition with a supplied block count. Require whole blocks in [0,255]; existingBlockChoices = blocks, newBlockChoices = 1, totalChoices = blocks+1.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| blocks | Blocks | Required. Safe integer; minimum 0; maximum 255. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| existingBlockChoices | Existing Block Choices | Required. Safe integer. |
| newBlockChoices | New Block Choices | Required. Safe integer. |
| totalChoices | Total Choices | Required. Safe integer. |
{
"input": {
"blocks": 3
},
"output": {
"existingBlockChoices": 3,
"newBlockChoices": 1,
"totalChoices": 4
}
}Limitations and assumptions
- This local choice count does not enumerate partitions or account for additional block constraints.
- 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.
- Partition Conjugate Single Column Height
Return one conjugate-partition column height.