Milliken–Taylor theorem
= Milliken–Taylor theorem
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The Milliken–Taylor theorem gives monochromatic systems of separated block sums with a fixed compressed coefficient vector, such as $(1,2,3)$. Systems associated with two nonproportional compressed coefficient vectors need not have the same color: in particular, there is a finite coloring for which a <finite-sums set> and the $(1,2,3)$ Milliken–Taylor system cannot be monochromatic together.