Intervals of balanced binary trees in the Tamari lattice

@article{Giraudo2012IntervalsOB,
  title={Intervals of balanced binary trees in the Tamari lattice},
  author={Samuele Giraudo},
  journal={Theor. Comput. Sci.},
  year={2012},
  volume={420},
  pages={1-27}
}
  • Samuele Giraudo
  • Published 18 July 2011
  • Computer Science, Mathematics
  • Theor. Comput. Sci.
Balanced binary trees in the Tamari lattice
TLDR
It is shown that the set of balanced binary trees is closed by interval in the Tamari lattice and the intervals (T0;T1) where T0 and T1 are balanced trees are isomorphic as posets to a hypercube.
A Motzkin filter in the Tamari lattice
Colored operads, series on colored operads, and combinatorial generating systems
Operads in algebraic combinatorics
TLDR
This work explores the aforementioned research direction and provides many constructions having the particularity to build algebraic structures on combinatorial objects, and develops for instance a functor from nonsymmetric colored operads to nons asymmetric operads, from monoids to operad, and from unitary magmas to nonsymmetrical operads.

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Balanced binary trees in the Tamari lattice
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It is shown that the set of balanced binary trees is closed by interval in the Tamari lattice and the intervals (T0;T1) where T0 and T1 are balanced trees are isomorphic as posets to a hypercube.
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