Arithmetree

Details Arithmetree Arithmetree

2001-12-04

arxiv.org/abs/math/0112034v1

J. of Algebra 258 (1), (2002), 275-309.

Mathematics

Combinatorics

34 pages

Scientific paper

We construct an addition and a multiplication on the set of planar binary trees, closely related to addition and multiplication on the integers. This gives rise to a new kind of (noncommutative) arithmetic theory. The price to pay for this generalization is that, first the addition is not commutative, second the multiplication is distributive with the addition only on the left. This algebraic structure is the "exponent part" of the free dendriform algebra on one generator, a notion related to several other types of algebras. In the second part we extend this theory to all the planar trees. Then it is related to the free dendriform trialgebra as constructed in Loday-Ronco's paper "Une dualite' entre simplexes standards et polytopes de Stasheff".

Affiliated with

Also associated with

No associations

Rating

Arithmetree 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 Arithmetree, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Arithmetree will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-479193