论文标题
$ g $标记功能，跨越树木和tutte多项式之间的广义射击图
Generalized Bijective Maps between $G$-Parking Functions, Spanning Trees, and the Tutte Polynomial
论文作者
论文摘要
我们介绍了一个称为树生长序列（TGS）的对象，以概括$ g $标记功能，跨越树和图形$ g $的tutte多项式中的一组单元。树生长序列确定可以应用于单个函数的算法，也可以应用于$ g $ parking函数的集合$ \ Mathcal {p} _ {g，q} $。选择后者时，该算法使用分裂操作 - 灵感来自Tutte多项式的递归质量 - 迭代$ \ Mathcal {p} _ {g，q} $中的$ \ mathcal {p} _;这将分别从$ \ Mathcal {p} _ {g，q} $分别从$ g $和tutte Monemials的生成树上产生$ \ Mathcal {p} _ {g，Q} $的$ρ$。我们将TGS算法与Dhar的算法和Chebikin和Pylyavskyy所描述的家人进行了比较。最后，我们使用类似的分裂操作来计算tutte多项式。
We introduce an object called a tree growing sequence (TGS) in an effort to generalize bijective correspondences between $G$-parking functions, spanning trees, and the set of monomials in the Tutte polynomial of a graph $G$. A tree growing sequence determines an algorithm which can be applied to a single function, or to the set $\mathcal{P}_{G,q}$ of $G$-parking functions. When the latter is chosen, the algorithm uses splitting operations - inspired by the recursive defintion of the Tutte polynomial - to iteratively break $\mathcal{P}_{G,q}$ into disjoint subsets. This results in bijective maps $τ$ and $ρ$ from $\mathcal{P}_{G,q}$ to the spanning trees of $G$ and Tutte monomials, respectively. We compare the TGS algorithm to Dhar's algorithm and the family described by Chebikin and Pylyavskyy. Finally, we compute a Tutte polynomial of a zonotopal tiling using analogous splitting operations.
