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.

A self-conjugate partition produces distinct odd diagonal hooks

Example

The partition

$λ = (5, 3, 3, 1, 1)$

is self-conjugate. Its diagonal cells are $(1, 1)$ , $(2, 2)$ , and $(3, 3)$ , and their hook lengths are

$9, 3, 1.$

Thus the diagonal-hook construction sends $λ$ to the distinct odd partition

$9 + 3 + 1.$

Depends on

Self-conjugate partitions correspond to distinct odd-part partitions

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

3 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.