A Tour of Chip-firing Games

Abstract: The term `chip-firing' can now be used to refer to any among a plethora of variants of a game, which, in its simplest form, is a discrete dynamical system with chips placed at the vertices of a connected graph, with the vertices being allowed to fire and send its chips to its neighbouring vertices, provided some degree conditions are met. Originating in the work of Bj{\"o}rner, Lov{\'a}sz and Shor (1991) (in the context of graphs) and Bak, Tang and Weisenfeld (1987) and Dhar (1999) (in the context of abelian sandpile models), there is now a rich literature on several variants of the game, spanning both its algebraic and combinatorial aspects.

We will have an overview of some recent work on `chip-firing', with a focus on its combinatorial connections with other ideas.

commutative algebraalgebraic topologycombinatorics

Audience: researchers in the topic

Applications of Combinatorics in Algebra, Topology and Graph Theory

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