12 research outputs found
Recommended from our members
Braid moves in commutation classes of the symmetric group
We prove that the expected number of braid moves in the commutation class of the
reduced word for
the long element in the symmetric group is one. This is a variant of a
similar result by V. Reiner, who proved that the expected number of braid moves in a random
reduced word for the long element is one. The proof is bijective and uses X. Viennot's
theory of heaps and variants of the promotion operator. In addition, we provide a
refinement of this result on orbits under the action of even and odd promotion operators.
This gives an example of a homomesy for a nonabelian (dihedral) group that is not induced
by an abelian subgroup. Our techniques extend to more general posets and to other
statistics
Braid moves in commutation classes of the symmetric group
24 pages; 5 figures; v3: version to appear in European J. CombinatoricsInternational audienceWe prove that the expected number of braid moves in the commutation class of the reduced word for the long element in the symmetric group is one. This is a variant of a similar result by V. Reiner, who proved that the expected number of braid moves in a random reduced word for the long element is one. The proof is bijective and uses X. Viennot's theory of heaps and variants of the promotion operator. In addition, we provide a refinement of this result on orbits under the action of even and odd promotion operators. This gives an example of a homomesy for a nonabelian (dihedral) group that is not induced by an abelian subgroup. Our techniques extend to more general posets and to other statistics