Almost tight lower and upper bounds on the maximum numbers of occurrences of various types of right rotations in a sequence of right rotations performed on a binary tree. In particular, the lower bound for right 2-turns refutes Sleator's Right Turn Conjecture.
A linear times inverse Ackerman upper bound for the Deque Conjecture. This bound is derived using the above upper bounds.
Two new proofs of the Scanning Theorem, one, a simple potential-based proof that solves Tarjan's problem of finding a potential-based proof for the theorem, the other, an inductive proof that generalizes the theorem.
AMS subject classification code (1991)68 P 05 68 R 05
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