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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.

3 votes

Conjecture of a subset of Wang tile which might be decidable

If you're interested in restriction of the domino problem to tile sets with some determinism properties, you might also be interested in this result about 4-way deterministic tile sets.
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2 votes

A sensitive 2-dimensional cellular automaton with a blocking word

Proposition 4 of this paper (mentionned by Ville Salo in the comments) does the following: given a Wang tile set that does not tile the plane but tiles a $n\times n$ finite square, it constructs a CA …
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