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.
Naming conventions for Burnside, Cauchy-Frobenius, and Redfield-Pólya
Remarks
This library's published orbit-counting result is Cauchy-Frobenius orbit counting: for a finite group action, so that is the name used in proofs on this page whenever the orbit average itself is cited.
The surrounding literature uses several other names for closely related statements. "Burnside's lemma" is the standard short name for the orbit count, while "Pólya's enumeration theorem" usually means the colouring-orbit specialization of that lemma through cycle structure. In the weighted setting, "Redfield-Pólya" or "Pólya's inventory theorem" is the more precise label for the pattern-inventory formula proved below.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
7 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
- Ben Lynn, Polya Theory: The Cycle Index Polynomial (standard reference, not scraped)
- Ben Lynn, Polya Theory: Pólya's Inventory Theorem (standard reference, not scraped)