DefinitionDefinition: Literature-sourcedProof: Not applicableSession-authored (Fable 5 assisted)judge pass (gpt-5.6-terra)audited 2026-08-26

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.

Orthogonal Latin squares and complete families of them

Definition

Let $L, M : R \times C \to S$ be Latin squares of the same order $n$ on the same row, column, and symbol sets. They are orthogonal when the map $(r, c) ⟼ (L (r, c), M (r, c))$ is a bijection from $R \times C$ to $S \times S$ , equivalently when every ordered pair of symbols occurs exactly once.

A complete family of mutually orthogonal Latin squares of order $n$ is a family of $n - 1$ pairwise orthogonal Latin squares of that order.

Depends on

A Latin square

Used by

Dependency tree · one level

1 result within one dependency step 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

Deductive Press, Section 16.2: Latin Squares and MOLS (standard reference, not scraped)