Order structure on the algebra of permutations and of planar binary trees
Combinatorics
2016-09-07 v1 Quantum Algebra
Abstract
In "Hopf algebra of the planar binary trees", Adv. Math. 139 (1998), no. 2, 293--309, we constructed by induction a graded associative product on the vector space generated by the planar binary trees (resp. the permutations). In the present paper we prove an explicit formula for this product in terms of a partial order on the set of planar binary trees (resp. the weak Bruhat order on the symmetric groups).
Keywords
Cite
@article{arxiv.math/0102066,
title = {Order structure on the algebra of permutations and of planar binary trees},
author = {Jean-Louis Loday and Maria O. Ronco},
journal= {arXiv preprint arXiv:math/0102066},
year = {2016}
}
Comments
19 pages