| R. Casas, J. D'iaz, and M. Verges. On counting BECs. Annals of Discrete Mathematics, 25:109--124, 1985. |
....For instance, Theorem 4.4. The average cost of running the simplification algorithm for an idempotent law on binary trees of size n is asymptotically linear as n tends to infinity. Many other statistics have been done on trees using this techniques. The tree compaction problem was studied in [CDV85, CDSV83] where it was introduced a nice generation of compacted trees. The analytical value was finally obtained in [FSS90] where they prove that the expected size of the maximally compacted representation of a random tree of size n is asymptotically c n p log n (1 O(1= log n) In the ....
R. Casas, J. D'iaz, and M. Verges. On counting BECs. Annals of Discrete Mathematics, 25:109--124, 1985.
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