On the number of hyperforests (Q1917608)

The author considers \(m\)-forests with \(n\) labeled vertices and \(T\) edges. Asymptotic expressions for the number of such hyperforests are obtained as \(m\) is fixed and \(n\), \(T \to \infty\) in such a manner that either \(0 < \alpha_0 \leq T/n \leq \alpha_1 < 1/(m(m - 1))\), where \(\alpha_0\) and \(\alpha_1\) are some constants, or \(T/n \to 1/(m(m - 1))\) sufficiently fast.