An article co-authored by Visiting Assistant Professor of Mathematics Dave Perkins was recently published in The Australasian Journal of Combinatorics. “A chip-firing variation and a Markov chain with uniform stationary distribution” presents results from a continuing study of burn-off chip-firing games on graphs.
A chip-firing game is played on a network of cells (for example, a checkerboard) that are connected along edges. A turn of a chip-firing game consists of dropping a “chip” on a random cell; if a cell’s chip pile is equal to at least the number of the cell’s neighbors, then one chip is distributed to each neighbor. This may trigger a chain reaction, and so these games are used in computer simulations to model earthquakes and avalanches.
Perkins and his co-author, P. Mark Kayll of the University of Montana, tweaked the rules and show that all chip distributions are, in the long run, equally likely. Kayll is also Perkins’ Ph. D. advisor.
An international, peer-reviewed journal, The Australasian Journal of Combinatorics is published for the Combinatorial Mathematics Society of Australasia by The University of Queensland’s Centre for Discrete Mathematics and Computing.