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.

A Latin square

Definition

Let $R$ , $C$ , and $S$ be finite sets of the same cardinality $n$ . A Latin square of order $n$ on rows $R$ , columns $C$ , and symbols $S$ is a function $L : R \times C \to S$ such that:

for each fixed row $r \in R$ , the map $c \mapsto L (r, c)$ is a bijection $C \to S$ ;
for each fixed column $c \in C$ , the map $r \mapsto L (r, c)$ is a bijection $R \to S$ .

When $R = C = S = {0, 1, \dots, n - 1}$ , this is the usual square array description.

Used by

A Latin square need not be orthogonal to an identical copy of itself Counterexample
Orthogonal Latin squares and complete families of them Definition
The linear Latin squares Lₐ(i,j)=ai+j over F_q are pairwise orthogonal Theorem

Dependency tree · 0 levels

Nothing. This result depends on no other item in the library.

Sources

Jonathan Davidson, Latin Squares (standard reference, not scraped)