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.

affine.partitions.lisp Lisp code run using Allegro Common Lisp from Franz.
affine.exceptional.types.mws Maple Worksheet

Sara Billey

Last modified: Fri Mar 14 11:03:43 PDT 2008