I'm currently dealing with inverted page tables and how they work. If I understood correctly, an IPT is a table that maps a frame number to a PID and page number. The way this works is by having a hash function map a tuple (PID, page_number) to (frame_number). If the entry of the table given by the frame number contains (PID, page), then we have a hit. Because a hash function can map multiple inputs to one output, we have to keep a chain of pages for each frame (according to my lecture notes).
Why does an inverted page table keep a linked list of pages per frame? Only one page can be loaded into a single frame at a time, how does this make sense? To me this seems more an issue similar to that of direct-mapped caching, where you have to throw out the previous block to make place for a new block.