ExampleConstruction: AI-generatedVerification: Not suppliedSession-authored (Fable 5 assisted)judge pass (gpt-5.6-terra)audited 2026-08-28

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Conjugation pairs the partitions of 6 by swapping length and largest part

Example

For the partitions of $6$ , conjugation gives the pairings

$6 \leftrightarrow 1 + 1 + 1 + 1 + 1 + 1,$

$5 + 1 \leftrightarrow 2 + 1 + 1 + 1 + 1,$

$4 + 2 \leftrightarrow 2 + 2 + 1 + 1,$

$4 + 1 + 1 \leftrightarrow 3 + 1 + 1 + 1,$

$3 + 3 \leftrightarrow 2 + 2 + 2,$

and

$3 + 2 + 1 \leftrightarrow 3 + 2 + 1.$

The fixed partition $3 + 2 + 1$ is self-conjugate.

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

4 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.