多类型分枝林的编码：分枝林总子代定律和计数法的应用
Coding multitype branching forests: application to the law of the total progeny of branching forest and to enumerations
摘要：
通过扩展的宽度优先搜索算法的任何d-型临界或亚临界不可约分支森林，我们表明，这样的森林可以通过d独立，整数值，d维随机游动编码。这种编码的应用程序与多元扩展的选票定理，这是证明在这里，使我们能够给出一个明确的形式的法律的总后代，连同每种类型的子树的数量，在后代分布的分支过程。然后，我们将这些结果应用到一些计数公式的多型森林与给定的程度和一个新的证明的拉格朗日-良好的反演定理。
英文摘要：
By extending the breadth first search algorithm to any d-type critical or subcritical irreducible branching forest, we show that such forests may be encoded through d independent, integer valued, d-dimensional random walks. An application of this coding together with a multivariate extension of the Ballot Theorem which is proved here, allow us to give an explicit form of the law of the total progeny, jointly with the number of subtrees of each type, in terms of the offspring distribution of the branching process. We then apply these results to some enumeration formulas of multitype forests with given degrees and to a new proof of the Lagrange-Good inversion Theorem.
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