Cyclic Decompositions of Affine PermutationsAlgebra & Discrete Mathematics
|Speaker:||Tom Denton, Fields Institute|
|Start time:||Tue, Jun 5 2012, 2:10PM|
We show that every affine permutation has a unique maximal decomposition into cyclically decreasing elements. This decomposition coincides with the Lehmer code, and contains a great deal of information about the permutation, such as length, descent set, and whether the permutation is fully-commutative. We will also demonstrate a new tableau model on the Lehmer code of the affine permutation, in which tableaux are in bijection with reduced expressions for the permutation.