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> (ii) linear functions are terrible where equi-label regions have a partitioned structure.

Could you explain what "equi-label regions having a partitioned structure" mean?

I missed a word "recursively", that I have edited in my original comment now.

Consider connected regions in the domain that have the same label. Much like countries on a political map. The situation where this has a short description in terms of recursive subdivision of space, is what I am calling a partitioned structure. It's really rather tautological.

"recursively partitioned" sounds like a fractal to me. Not sure what you really mean.
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