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We consider partitions of $\mathbb{F}_q^n$ into affine subspaces, giving several examples of constructions which are irreducible in the sense that no nontrivial subpartition is a partition of an affine subspace. Our work leaves many interesting questions open.

The work is part of a three paper series. The second part is about partitions of $\{0,1\}^n$ into subcubes, and the third part is about relations to proof complexity.