Weak Bruhat order on the set of faces of the permutahedra

Details Weak Bruhat order on the set of faces of the permutahedra Weak Bruhat order on the set of faces of the permutahedra

2004-04-20

arxiv.org/abs/math/0404352v1

Mathematics

Combinatorics

30 pages

Scientific paper

We extend the weak Bruhat order of a finite Coxeter group to the set of its
coclasses, modulo parabolic standard subgroups. We use this order to describe
associative algebra structures on the vector spaces spanned by the faces of
permutahedra on one side, and on the vector space spanned by the planar rooted
trees, on the other one.

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