= Colour profile of a finite block
{title2=$(c(b_1),\ldots,c(b_N))$}
= Color profile of a finite block
{synonym}
= Colour profile
{synonym}
= Color profile
{synonym}
The <colour profile> of a length-$N$ block $b_1,\ldots,b_N$ under a <finite colouring> $c$ is the ordered tuple $(c(b_1),\ldots,c(b_N))$. There are at most $r^N$ profiles when $c$ uses at most $r$ colours. Equally profiled blocks reproduce every colour configuration at the same relative positions; this converts a colouring of points into a <finite colouring> of blocks in the <colour-focusing proof of Van der Waerden theorem>.
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