（G，m）-多停车场函数
(G,m)-multiparking functions
摘要：
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 $m\in V(G)$ . 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 $\mathcal{F}_{G,m}$ 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 $\sum\limits_{i=1}^na_i$ of $G$ -parking functions $(a_1,...,a_n)$ .
英文摘要：
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 $m\in V(G)$. 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 $\mathcal{F}_{G,m}$ 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 $\sum\limits_{i=1}^na_i$ of $G$-parking functions $(a_1,...,a_n)$.
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