Concept

Latin square

A square array in which every symbol appears exactly once in each row and each column. It is the multiplication table of a quasigroup, and the question of when two can be superimposed with all symbol pairs distinct is two centuries old.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

Also named here as transversal — the same set of essays touches all of them, so they are one junction rather than several.

Transversals of the cyclic square of order 6. A cyclic Latin square with a transversal marked if it has one, beside a count of transversals at neighbouring orders.

The thirty-six officers

Six regiments send six officers each, one of every rank. Arrange all thirty-six in a square so that each row and each column holds every rank once and every regiment once. Euler could not, guessed why, and was wrong about the reason.

computation · latin squares

A matching that covers all 5 of one side. A bipartite graph with every possible pairing drawn thin and one complete matching drawn thick, so that each vertex on the left is joined to a distinct vertex on the right.

One bottleneck and nothing else

A set of jobs can be filled by distinct people unless some group of jobs has too few candidates between them — and that single obstruction is the only one there is, which is what makes the theorem worth having.

discrete · halls theorem

Named alongside it

The objects these essays reach for when they reach for this one.

Counting argument Existence proof Transversal Counterexample Deficiency Finite field Graph Matching Orthogonal latin squares Pigeonhole principle Projective plane

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