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I read these two sentences:

Such an array is said to be h-sorted. Put another way, an h-sorted array is h independent sorted sub-sequences, interleaved together.

I don't know the grammar behind "h-sorted" and "h independent sorted". And why is it not "h independently" sorted? For the source please refer to this link.

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The writer is saying that an h sorted array can be defined as a set of h independently sorted subsequences, combined (interleaved).

As written you would just interpret this as some number h of independent (of each other), sorted subsequences. However I agree the adverb independently seems more appropriate than the adjective independent in this context, and it's also unclear why he uses the variable h rather than the more typical variable n ... but perhaps these are just typical jargon in this academic field, or when writing about this subject.

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