Algebraic Combinatorics

Here is a worksheet to create abacus diagrams and core partitions in Affine A. Change the level of the beads on the abacus to determine the corresponding core partition and Coxeter length.
Combinatorics of Type A

Here is a worksheet to create abacus diagrams and core partitions in Affine C. Change the level of the beads on the abacus to determine the corresponding core partition and Coxeter length.
Combinatorics of Type C

Here is an animation of the building of an abacus and core partition one generator at a time in Type C.
Abacus/Core Example

Here is an animation of root lattice coordinates and their alcoves which correspond to simultaneous core partitions.
Roots and Cores

Chemistry

Here is a visualization of MgO nanotubes.
MgO Nanotubes

Here is a visualization of nanotubes and the Madelung Constants of their individual ions.
Madelung Constants for ions in nanotubes