Learn Swedish: Kaptenen på fartygets hytt är liten. - The captain of the ship's cabin is small.

This is the phrasal genitive (gruppgenitiv) in action. Instead of attaching the -s to the owner (kaptenen), Swedish attaches it to the very last word of the entire descriptive phrase (kaptenen på fartyget). It works exactly like the English phrase 'the captain of the ship's'.

We are talking about a specific cabin, so why is it hytt instead of the definite hytten?

Whenever a noun directly follows a genitive -s or a possessive word, it must take the indefinite form. The possessive ending on fartygets already points to a specific cabin, so adding the definite -en ending to hytt would be grammatically redundant in Swedish.

Why use the preposition på here instead of av to mean 'of the ship'?

Swedish rarely uses av to show possession or affiliation the way English uses 'of'. When referring to someone's role, job, or position at a workplace, institution, or aboard a large vehicle like a ship, you generally use på.

Because fartyget is an ett-word, shouldn't the adjective be litet instead of liten?