Order structure on the algebra of permutations and of planar binary trees

Details Order structure on the algebra of permutations and of planar binary trees Order structure on the algebra of permutations and of planar binary trees

2001-02-08

arxiv.org/abs/math/0102066v1

J. Algebraic Combin. 15 (2002), no. 3, 253-270.

Mathematics

Combinatorics

19 pages

Scientific paper

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).

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