## Improved Encoding and Counting of Uniform Hypertrees. (arXiv:1711.03335v1 [math.CO])

We consider labeled $r$-uniform hypertrees having $n \ge r$ vertices. The number of hyperedges in such a hypertree is $m = (n - 1)/(r - 1)$. We show that there are exactly $f(n, r) = \frac{(n-1)! n^{m-1}}{m! (r-1)!^m}$ $r$-uniform hypertrees with $n$ labeled vertices. 查看全文>>