I am reading Multiagent Systems by Yoav Shoham, and in chapter 5 about extensive games, the definition of imperfect-information games extends the perfect-information games definition with equivalence classes.
But it is also mentioned that,
"Perfect-information games can be thought of as a special case of imperfect- information games, in which every equivalence class of each partition is a singleton. "
I understand what equivalence classes being singleton for players would make it a perfect-information game, but what is a partition that's mentioned here?
In this Example Game Tree, I know that player 1 has two equivalence classes - first at the root node (so only one decision node) with available actions L and R, and the second with two decision nodes with actions l and r. Player 2 has one equivalence class of one decision node with actions A and B.
What are the partitions in this example? I am having a difficult time relating the two ideas.
Edit: I have attached the definition they have given for imperfect-information games