I have used Mathematica to create some interactive worksheets from my research.
In order to see them, you will need to download the free Wolfram
CDF viewer. It's worth it, really.
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
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