Is the construction "noun- and adverb adjective noun" correct?
Example: "we found a significant difference between human- and algorithmically generated summaries".
This is a question about suspended compounds:
like: short- and long-term interest rates or second- and third-class tickets. The adjective can be a past participle too: funded- and unfunded-pension plans. There is a space after the first dash.
human- and animal-generated waste. [just to show the dashes]
When you have two nouns, both of which are connected to the past participle, you need two dashes with a space after the first one.
Therefore, I would write your phrase like this:
human- and algorithm-generated summaries
You do not need an adverb. The noun algorithm works just fine.
Summaries generated by algorithm=algorithm-generated summaries.
We found a significant difference between human- and algorithmically generated summaries.
That sentence invites that unnatural awkwardness upon itself. It could be easily avoided:
We found a significant difference between summaries generated by humans and those generated by algorithms.
There is no reason to reject such a sentence on the grounds that it repeats a word or phrase, whereas this concoction human- and algorithmically generated is something of a monstrosity.
So take your pick, a bit of repetition or a train-wreck of a modifier.
P.S. Let me add that this rejection of a phrase because it is repetitive is a bugbear of programmers especially, and there are quite a lot of them on this site. They should not apply their peculiar sense of parsimony to natural language.
P.P.S. And let me also add that you will find this sort of hyphenated combination in the wild. I don't dispute that it is grammatical. But I do think it is crappy writing. It does absolutely nothing to enhance clarity—in fact it does the opposite—and there is no real justification for it.