Alphabeta MathHow 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.
The generating-function proof and Glaisher's bijection prove the same Euler theorem
Remarks
Euler's theorem by generating functions proves Euler's theorem by identifying two formal products and then comparing coefficients. Glaisher's bijection between odd-part and distinct-part partitions proves the same equality by explicitly transporting one partition family to the other.
The two routes therefore agree in the strongest possible sense: one gives coefficientwise equality of generating series, the other gives an actual bijection on each size- layer. The page keeps both because they use different ideas, not because they assert different numerical claims.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
6 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.
Sources
- Darij Grinberg, Enumerative Combinatorics: class notes (standard reference, not scraped)
- Stephen Melczer, An Invitation to Enumeration, Chapter 9: Integer Partitions (standard reference, not scraped)