Annotating Kimmo Eriksson’s Poem

“Start counting her NUMBER OF FACES,” Kimmo Eriksson, Brush up your Björner (2008).

The time is right to annotate Kimmo Eriksson’s memorable poem:

1. What are Chip firing games?

Many women will find it admirable
if you tell her she makes your CHIPS FIRABLE.

Chip firing games are (solitary) games played on graphs: each node of a directed graph contains a pile of chips. A move consists of selecting a node with at least as many chips as its outdegree, and sending one chip along each outgoing edge to its neighbors. The remarkable property of these games is that depending on the sizes of the piles, either the game continues forever or it reaches a position where it cannot be played further. In the latter case the final position, the number of moves, and even the number of times each node fired do not depend on the specific moves made along the game.

Sheep firing game (You may play the game by clicking on the picture; disclaimer: we object to cruel treatment of animals)

In the rest of this post you can read about shellability, weak and strong (Bruhat) partial orders on the set of permutations, chessboard complexes, and more.  Continue reading