2004/08/25 by Philippe Leroux, Leroux Philippe, Philippe, Leroux
Computer Science · Mathematics · #05C05 #06A07 #11A99 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Polynomial and algebraic computation #Quantum Algebra (math.QA) #Topological and Geometric Data Analysis #math.CO #math.QA #msc:05C05 #msc:06A07 #msc:11A99
paper · pdf · doi:10.48550/arxiv.math/0408349
19 pages
arxiv created 2004/08/25 · openalex publication_date 2004/08/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.