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

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

2004-08-25

arxiv.org/abs/math/0408349v1

Mathematics

Combinatorics

19 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

A LL-lattice reformulation of arithmetree over planar rooted trees. Part II does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A LL-lattice reformulation of arithmetree over planar rooted trees. Part II, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A LL-lattice reformulation of arithmetree over planar rooted trees. Part II will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-338925