The chip-firing game is a simple game with only one move. Starting with a collection of poker chips on the vertices of a graph, one is allowed to move them around the graph using what is known as the "chip-firing move". A version of this game can be found here. Despite its simplicity, this game has deep connections to dynamics, number theory, and algebraic geometry.
The gonality of a graph is the smallest number of chips required so that the chip-firing game is always winnable. In his PhD thesis, recent UK graduate Noah Speeter computed the gonality of a special family of graphs, known as rook graphs. In this project, we will attempt to generalize Speeter's results to Ferrer's rook graphs, which are like a non-rectangular analogue of rook graphs. This project will focus heavily on examples.
The gonality of graphs has attracted recent interest, due to its connection to the geometry of algebraic curves. Rook graphs are of particular interest because of their relation to the geometry of complete intersection curves.
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