So this is just 'pool towels-the'. Why is there no genitive anywhere. The towels for the pool, or of the pool'
It's the Turkish equivalent of a compound word. If you want to specify that they're the pool towels (you're basically using "pool" as an adjective to describe "towels"), you leave the first noun alone, and put a possessive ending on the second one. There's more here: https://www.duolingo.com/comment/8616301
OK, that's helpful. I had read that, but ages ago. So dog bed would be köpek yatagi?(with the right characters)
Exactly. (I hadn't had to figure out "dog bed" in Turkish, yet, so I asked Google to find me a köpek yatağı, to double check. And lo, and behold: https://www.google.com/?gws_rd=ssl#q=k%C3%B6pek+yata%C4%9F%C4%B1 =) )
thanks ... but why can't we say primarily (pool's towels) ===> (havuzun havlusı)
The pronunciation of havluları sounds like she's saying havlulede though that's not a word, it certainly doesn't help.
Because "havuz" is in the nominative case, and not in the genitive case. In order to be "the pool's towels," "havuz" needs to be possessive, so it has to have a "-un" ending: "havuzun havluları."
When the first noun in the nominative case (not the genitive) and there's a possessive ending on the second noun, it's just a compound noun: "pool towels."