完全超图上的超森林的Grassmann积分表示
Hyperforests on the Complete Hypergraph by Grassmann Integral Representation
摘要：
研究了一般n阶完全超图中有根和无根超森林的生成函数，给出了它们的生成函数的一种新的Grassmann表示。我们表明，这种新的方法编码的指数生成函数的不同数量的顶点的已知结果。我们还考虑了一些应用，如计数超森林的k-一致完全超图和一个完全的超边的所有维。讨论了连通分支数多的渐近区域的一些一般性质。
英文摘要：
We study the generating function of rooted and unrooted hyperforests in a general complete hypergraph with n vertices by using a novel Grassmann representation of their generating functions. We show that this new approach encodes the known results about the exponential generating functions for the different number of vertices. We consider also some applications as counting hyperforests in the k-uniform complete hypergraph and the one complete in hyperedges of all dimensions. Some general feature of the asymptotic regimes for large number of connected components is discussed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
