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28 March 2024
 
  » arxiv » 0810.1130

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(G,m)-multiparking functions
Hungyung Chang ; Po-Yi Huang ; Jun Ma ; Yeong-Nan Yeh ;
Date 7 Oct 2008
AbstractThe 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 $min V(G)$. 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 $sumlimits_{i=1}^na_i$ of $G$-parking functions $(a_1,...,a_n)$.
Source arXiv, 0810.1130
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