About the phrase "combinatorial characterization"

Asked Sep 25 '22 at 05:58

Active Sep 25 '22 at 06:22

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What does the phrase "combinatorial characterization" mean? Does it mean "discrete", regardless of topological concepts? I don't know, I would appreciate your kind answer. For example, a subshift is a subset $X\subset A^G$ closed and invariant, but the subshifts have a combinatorial characterization: equivalently we found a finite set of patterns $\mathcal{F}$ such that $$X=\{x\in A^G: P\sqsubset x \Rightarrow P\notin \mathcal{F}\}.$$

What other uses do you know for this phrase?

edited Sep 25 '22 at 06:22

asked Sep 25 '22 at 05:58

Mike Sanz

1

It would be clearer if you gave context; where did you see this? Can you quote an excerpt? – Qiaochu Yuan Sep 25 '22 at 06:04
Do you mean combinatorial proof ? – Jean Marie Sep 25 '22 at 06:22
Any connection to Sperner's theorem ? – Jean Marie Sep 25 '22 at 06:25
What are $A$ and $G$ in notation $A^G$ ? – Jean Marie Sep 25 '22 at 06:38
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$A$ is a set with the discrete topology, $G$ is a group and $A^G$ represents the set of maps of the form $G\to A$ with the product topology. – Mike Sanz Sep 25 '22 at 06:42

About the phrase "combinatorial characterization"

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