 A-invariant coloring of a Cartesian power (source code)

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= A-invariant coloring of a Cartesian power
{title2=$A$-invariant coloring of a Cartesian power}

For $A\subseteq X$, a coloring of $X^n$ is $A$-invariant when changing any coordinates from one member of $A$ to another does not change the color. A product argument upgrades the existence of a copy of $X$ on which $A$ is monochromatic to an $A$-invariant copy of every finite Cartesian power $X^n$.

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