Irreducible subcube partitions

Yuval Filmus, Edward Hirsch, Sascha Kurz, Ferdinand Ihringer, Artur Riazanov, Alexander Smal, Marc Vinyals
Elec. J. Comb.

We consider partitions of $\{0,1\}^n$ into subcubes, giving several examples of constructions which are irreducible in the sense that no nontrivial subpartition is a partition of a subcube. Our work leaves many interesting questions open.

The work is part of a three paper series. The first part is about partitions of $\mathbb{F}_q^n$ into affine subspaces, and the third part is about relations to proof complexity.


 title = {Irreducible subcube partitions},
 author = {Yuval Filmus and Edward Hirsch and Sascha Kurz and Ferdinand Ihringer and Artur Riazanov and Alexander Smal and Marc Vinyals},
 journal = {Elec. J. Comb.},
 volume = {30},
 number = {3},
 pages = {P3.29},
 date = {2023}
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