Applications of the Brauer complex: card shuffling, permutation statistics, and dynamical systems
| dc.creator | Fulman, Jason | |
| dc.date | 2001-02-14 | |
| dc.date | 2001-05-09 | |
| dc.date.accessioned | 2026-07-07T04:40:09Z | |
| dc.date.available | 2026-07-07T04:40:09Z | |
| dc.description | By algebraic group theory, there is a map from the semisimple conjugacy classes of a finite group of Lie type to the conjugacy classes of the Weyl group. Picking a semisimple class uniformly at random yields a probability measure on conjugacy classes of the Weyl group. Using the Brauer complex, it is proved that this measure agrees with a second measure on conjugacy classes of the Weyl group induced by a construction of Cellini using the affine Weyl group. Formulas for Cellini's measure in type $A$ are found. This leads to new models of card shuffling and has interesting combinatorial and number theoretic consequences. An analysis of type C gives another solution to a problem of Rogers in dynamical systems: the enumeration of unimodal permutations by cycle structure. The proof uses the factorization theory of palindromic polynomials over finite fields. Contact is made with symmetric function theory. | |
| dc.description | One change: we fix a typo in definition of f(m,k,i,d) on page 14 | |
| dc.identifier | https://arxiv.org/abs/math/0102105 | |
| dc.identifier | http://arxiv.org/abs/math/0102105 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60937 | |
| dc.subject | Combinatorics | |
| dc.subject | Dynamical Systems | |
| dc.subject | Group Theory | |
| dc.title | Applications of the Brauer complex: card shuffling, permutation statistics, and dynamical systems | |
| dc.type | text |