Code for Affine Partitions
Below is the code used to supplement the proofs in "Affine Partitions and Affine
Grassmannians" by Sara Billey and Stephen Mitchell. The code
includes algorithms for generating elements in Coxeter groups up
to some length, the Coxeter matrices for Weyl groups and Affine
Weyl groups, algorithms for quotients of Coxeter groups, affine
partitions, colored partitions, rank generating functions, Bruhat
order, weak order, generalized Young's lattice, etc.
The code is supplements the proofs in the paper by proving that the
affine partitions in each exceptional type are equinumerous with
the minimal length coset representatives for the affine Weyl
group mod the Weyl group. The lisp code can be used to identify
the generating function for affine partitions. The maple code
takes in this generating function, simplifies it, and compares
it with Bott's formula.
Last modified: Fri Mar 14 11:03:43 PDT 2008