[cracauer]

And that's just the fares. We didn't talk yet about seat availability.

You have to ask for seat availability for the complete fare-component, the thing that a fare covers. So if you go Boston-Copenhagen-Hamburg you don't just do seat queries for Bos->CPH and CPH->BOS, you are required to ask those questions in a context that says you travel BOS->HAM.

The seat availability for the same seats on the same flights on the BOS->CPH leg is different depending on whether you ask in a BOS->CPH context or a BOS->HAM context.

You can see how asking all those seat availability queries for all the different ways to fly in the query explodes nicely. Combinatorics at work.