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Cyclic Decompositions of Affine Permutations
Algebra & Discrete Mathematics| Speaker: | Tom Denton, Fields Institute |
| Location: | 2112 MSB |
| Start time: | Tue, Jun 5 2012, 2:10PM |
Description
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.