Graham–Rothschild: Ramsey theorem for parameter sets

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Library card.

R. L. Graham and B. L. Rothschild, "Ramsey's theorem for $n$-parameter sets," Transactions of the American Mathematical Society 159 (1971), 257--292.

The Graham–Rothschild theorem says that if the k-parameter subsets of a sufficiently large n-parameter set are divided into r classes, some l-parameter subset has all its k-parameter subsets in one class (in later language, finite colorings of parameter words contain monochromatic parameter subspaces). It is the general product/variable-word engine behind many finite Ramsey constructions.