I am generally ok with the accents of 1st and 2nd declension nouns and with the recessive accents of verbs, but participles got me confused. Consider, for example, the middle/passive present tense participles of λύω, and consider in particular the feminine λυομένη, whose genitive plural is λυομένων. Now, I would have expected a circumflex on the ultima because I thought a circumflex on the ultima was a rule for 1st declension nouns. Perhaps a participle does not count as a noun, but if so, how do we determine the accent for participles? Is it recessive like verbs, is it persistent like nouns, or even a combination of both?
The rules for the accentuation of participles vary depending on the type of participle. For middle/passives, the accent is persistent on the syllable preceding the participial suffix.
Check Smyth §209. The feminine pl. genitive is accented like the masculine pl. gen, thus λυομένων. This also applies to 1st/2nd declension adjectives ending in -ος,-η,-ον. The feminine sg. λυομένη takes the acute on the penult because the ultima is long.