When I was playing Tangerine Tycoon, I thought, "Why do people always write 'ae^b' for ? 10 is of course not e!" Then, I found "change notation" button, so I pressed it several times to get "right" expression.
While pressing the button, I found something strange:
a ( Y ) b
This is called "butt notation" and there is even an achievement for finding this.
Now, stop playing the game and start the googology.
Definition: //Y is not a variable but a part of the notation.
(Y) is right-associative because that's bigger than the left one.
Yeah, the same pattern as up-arrow notation comes in.