A LL-lattice reformulation of arithmetree over planar rooted trees. Part II
| dc.creator | Philippe, Leroux | |
| dc.date | 2004-08-25 | |
| dc.date.accessioned | 2026-07-07T05:11:34Z | |
| dc.date.available | 2026-07-07T05:11:34Z | |
| dc.description | 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. | |
| dc.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/math/0408349 | |
| dc.identifier | http://arxiv.org/abs/math/0408349 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72283 | |
| dc.subject | Combinatorics | |
| dc.subject | Quantum Algebra | |
| dc.subject | 05C05; 06A07; 11A99 | |
| dc.title | A LL-lattice reformulation of arithmetree over planar rooted trees. Part II | |
| dc.type | text |