Explanation

The "why" of Enumlib. Conceptual scaffolding for the underlying math, the algorithms drawn from the Hart-Forcade-Nelson papers, and the dispatch logic that picks the right one for your problem. Read these for mental-model purposes; for "how do I run X" see the How-to guides, and for "what's the API of Y" see the Reference.

Start here

• Algorithm overview — bird's-eye view of the four enumeration algorithms and the Pólya counter.
• Glossary — compact term reference for the rest of these pages.

The four algorithms

• Exhaustive enumeration (HF 2008) — the original algorithm. Iterate every coloring; canonicalize each. The reference implementation; not :auto's default.
• Multinomial mixed-radix hash (HF 2012) — iterate only colorings at the target concentration. Includes the §A.1 site-mask variant (:multinomial_restricted) for Regime C (heterogeneous sublattices).
• Recursive stabilizer (Morgan-Hart 2017) — the tree. Doesn't need a bitmap; :auto's default for almost everything.

Counting and the resource check

• Pólya counting — Burnside on coloring spaces, plus the Möbius-inversion correction for aperiodic orbits.
• Dispatch and the resource check — how algorithm = :auto picks; how the enumeration resource check refuses oversized requests.

Policy

• Super-periodicity — why colorings periodic on a smaller supercell are dropped by default.
• Concentration and multiplicity — the type layer above HF 2012, plus the divisibility-skip semantics.