Name
Abstract | ||
|---|---|---|
We prove that the expected number of braid moves in the commutation class of the reduced word (s1s2sn1)(s1s2sn2)(s1s2)(s1) for the long element in the symmetric group Sn 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.Viennots 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. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1016/j.ejc.2016.10.008 | Eur. J. Comb. |
Field | DocType | Volume |
Braid theory,Discrete mathematics,Abelian group,Combinatorics,Braid,Bijection,Symmetric group,Expected value,Operator (computer programming),Braid group,Mathematics | Journal | 62 |
Issue | ISSN | Citations |
C | 0195-6698 | 1 |
PageRank | References | Authors |
0.38 | 9 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Anne Schilling | 1 | 17 | 6.74 |
| Nicolas M. Thiéry | 2 | 12 | 4.66 |
| graham white | 3 | 1 | 0.38 |
| nathan williams | 4 | 1 | 1.06 |