Identity Configurations of the Sandpile Group

Authors

William Chen '06, Illinois Mathematics and Science Academy

Files

Description

The abelian sandpile model on a connected graph yields a finite abelian group Q of recurrent configurations which is closely related to the combinatorial Laplacian. We consider the identity configuration of the sandpile group on graphs with large edge multiplicities, called “thick” graphs. We explicitly compute the identity configuration for all thick paths using a recursion formula. We then analyze the thick cycle and explicitly compute the identity configuration for the three-cycle, the four-cycle, and certain types of symmetric cycles. The latter is a special case of a more general symmetry theorem we prove that applies to an arbitrary graph.

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.

Publication Date

11-15-2005

Disciplines

Mathematics

Comments

2006 Semifinalist of the 65th Science Talent Search

Recommended Citation

Chen, William '06, "Identity Configurations of the Sandpile Group" (2005). Distinguished Student Work. 2.
https://digitalcommons.imsa.edu/sci_dsw/2