The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Foundations of Computer Science
Foundations of Computer Science
Introduction to Algorithms
Order Structure on the Algebra of Permutations and of Planar Binary Trees
Journal of Algebraic Combinatorics: An International Journal
Functional Equations for Data Structures
STACS '88 Proceedings of the 5th Annual Symposium on Theoretical Aspects of Computer Science
The algebra of binary search trees
Theoretical Computer Science - Combinatorics on words
The Art of Computer Programming, Volume 4, Fascicle 4: Generating All Trees--History of Combinatorial Generation (Art of Computer Programming)
Intervals in Catalan lattices and realizers of triangulations
Journal of Combinatorial Theory Series A
Analytic Combinatorics
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We show that the set of balanced binary trees is closed by interval in the Tamari lattice. We establish that the intervals [T,T^'], where T and T^' are balanced binary trees are isomorphic as posets to a hypercube. We introduce synchronous grammars that allow to generate tree-like structures and obtain fixed-point functional equations to enumerate these. We also introduce imbalance tree patterns and show that they can be used to describe some sets of balanced binary trees that play a particular role in the Tamari lattice. Finally, we investigate other families of binary trees that are also closed by interval in the Tamari lattice.