The chip-firing game
Lilla Tóthmérész · Eötvös Loránd Tudományegyetem · 2017
Proposition 1.1.4.For a strongly connected digraph G there exists a unique prim-i=1 λ i p i , where for i ∈ {1, . . ., k}, λ i ∈ Z and p i is the primitive period vector of G i restricted to V (G i ) and zero elsewhere.Definition 1.3.1 (The rank of a divisor, [5]).When we wish to emphasize the underlying graph, we write rank G (f ) instead of rank(f ).The following is a straightforward consequence of Proposition 1.4.1.Corollary 1.4.2.For any f ∈ Div(G) on a strongly connected digraph G, the following holds: