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We use a novel decomposition to create succinct data structures -- supportinga wide range of operations on static trees in constant time -- for a varietytree classes, extending results of Munro, Nicholson, Benkner, and Wild.Motivated by the class of AVL trees, we further derive asymptotics for theinformation-theoretic lower bound on the number of bits needed to store treeclasses whose generating functions satisfy certain functional equations. Inparticular, we prove that AVL trees require approximately $0.938$ bits per nodeto encode.

Enumeration and Succinct Encoding of AVL Trees