That conference proceedings I ordered from library storage came yesterday, and I picked it up today. Apparently the combinatorial species equations that generate AVL trees are
A(X) = U(X,X)
U(X,Y) = X + U(X2 + 2XY, X)
But I can't figure out exactly why. Certainly I have a clue as to why the X2 + 2XY is in there, since it must correspond to the fact that an AVL tree of height h is made out of two such trees each of height h-1, or one tree of height h-1 and one of h-2. So I nearly grasp that X stands for AVL-tree-of-height-h-1 and Y is AVL-tree-of-height-h-2, but somehow I can't make everything else line up right. Unfortunately the cited article that explains the whole story is (a) in a library not open on the weekends, and (b) (it should be noted this is a much more permanent problem) very probably in French.
Today was actually productive since
platypuslord and I wrote up our project proposal for the kleinberg class. After that I putzed around Hillman some, read (and enjoyed very much) some of Virginia Woolf's "Moments of Being" (whence that quote last post), watched Fellini's "8 1/2" with the generalists (very strange film, seemed interesting but too long to really hold my attention; Anouk Aimée, the actress that played Luisa, was incredible, though) and finally wandered by the cs lounge and got sucked into a game of poker (in which I profited the tidy sum of $0.45).
A(X) = U(X,X)
U(X,Y) = X + U(X2 + 2XY, X)
But I can't figure out exactly why. Certainly I have a clue as to why the X2 + 2XY is in there, since it must correspond to the fact that an AVL tree of height h is made out of two such trees each of height h-1, or one tree of height h-1 and one of h-2. So I nearly grasp that X stands for AVL-tree-of-height-h-1 and Y is AVL-tree-of-height-h-2, but somehow I can't make everything else line up right. Unfortunately the cited article that explains the whole story is (a) in a library not open on the weekends, and (b) (it should be noted this is a much more permanent problem) very probably in French.
Today was actually productive since
platypuslord and I wrote up our project proposal for the kleinberg class. After that I putzed around Hillman some, read (and enjoyed very much) some of Virginia Woolf's "Moments of Being" (whence that quote last post), watched Fellini's "8 1/2" with the generalists (very strange film, seemed interesting but too long to really hold my attention; Anouk Aimée, the actress that played Luisa, was incredible, though) and finally wandered by the cs lounge and got sucked into a game of poker (in which I profited the tidy sum of $0.45).