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(G,m)-multiparking functions | Hungyung Chang
; Po-Yi Huang
; Jun Ma
; Yeong-Nan Yeh
; | Date: |
7 Oct 2008 | Abstract: | 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 $min V(G)$. 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 | Services: | Forum | Review | PDF | Favorites |
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