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A LL-lattice reformulation of arithmetree over planar rooted trees. Part II

Leroux Philippe
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Abstract

We continue our reformulation of free dendriform algebras, dealing this time with the free dendriform trialgebra generated be Y over planar rooted trees. We propose a 'deformation' of a vectorial coding used in Part I, giving a LL-lattice on rooted planar trees according to the terminology of A. Blass and B. E. Sagan. The three main operations on trees become explicit, giving thus a complementary approach to a very recent work of P. palacios and M. Ronco. Our parenthesis framework allows a more tractable reformulation to explore the properties of the underlying lattice describing operations and simplify a proof of a fundamental theorem related to arithmetics over trees, the so-called arithmetree. Arithmetree is then viewed as a noncommutative extention of (N,+,x), the integers being played by the corollas. We give also two representations of the super Catalan numbers or Schroder numbers.

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Leroux Philippe. 2004-08-25. A LL-lattice reformulation of arithmetree over planar rooted trees. Part II. https://arxiv.org/abs/math/0408349

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