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.

Glaisher's bijection on an odd-part partition

Example

Start with the odd-part partition

$5 + 5 + 3 + 1 + 1.$

Its multiplicities are

$2 = 2^{1} for the part 5, 1 = 2^{0} for the part 3, 2 = 2^{1} for the part 1.$

Glaisher's rule therefore replaces the two $5$ 's by one $10$ , keeps the $3$ , and replaces the two $1$ 's by one $2$ . The image is the distinct-part partition

$10 + 3 + 2.$

Depends on

Glaisher's bijection between odd-part and distinct-part partitions

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

2 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.