2008/10/07 by Chang, Hungyung, Huang, Po-Yi, Ma, Jun +1
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.0810.1130
The conceptions of G-parking functions and G-multiparking functions were introduced in [15] and [12] respectively. In this paper, let G be a connected graph with vertex set \1,2,...,n\ and m∈ V(G). We give the definition of (G,m)-multiparking function. This definition unifies the conceptions of G-parking function and G-multiparking function. We construct bijections between the set of (G,m)-multiparking functions and the set of FG,m of spanning color m-forests of G. Furthermore we define the (G,m)-multiparking complement function, give the reciprocity theorem for (G,m)-multiparking function and extend the results [25,12] to (G,m)-multiparking function. Finally, we use a combinatorial methods to give a recursion of the generating function of the sum ∑i=1nai of G-parking functions (a1,...,an).