ChipFiring.jl is a Julia package for analyzing chip-firing games on graphs. The codes are roughly based on the algorithms given in Sandpiles and Divisors: An Introduction to Chip-Firing by Corry and Perkinson (2018). A key objective is for the package to be useful for both researchers and students. Its features include:

• Basic operations on chip-firing graphs (e.g. firing, lending)
• Computations of $r$-th graph gonality
• Uniform subdivisions of graphs
• Rank computations
• q-reduction, Dhar's burning algorithm, and equivalence
• Conversion from graph6 format

This package is on the official Julia registry and can be installed via Pkg.add(ChipFiring). For more details, see the documentation here.

julia> multiplicity_matrix = [
    0 2 0 1;
    2 0 1 0;
    0 1 0 1;
    1 0 1 0   
]
[output omitted]

julia> g = ChipFiringGraph(multiplicity_matrix)
Graph(V=4, E=5, Edges=[(1, 2), (1, 2), (1, 4), (2, 3), (3, 4)])

julia> compute_gonality(g)
2

julia> d = Divisor([1, 1, 1, 1])
Divisor([1, 1, 1, 1])

julia> q_reduced(g, d, 1)
Divisor([-4, 1, 1, 0])

This package was developed during the SMALL 2025 REU hosted at Williams College, funded by NSF Grant DMS2241623. Special thanks to Charlotte Chen, Benham Cobb, Ralph Morrison, Noam Pasman, Madeline Reeve, for contributing code and/or feedback.