Questions tagged [combinatorial-species]

For questions concerning the theory and applications of combinatorial species, the endofunctors of the category of finite sets and bijections, and the calculus thereof.

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Finding the number of surjective distributions

I have been stuck with the following problem for hours, and I was hoping someone could give me a hint to attack it. Thanks! We define a distribution as a function together with a linear ordering on ...
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A Closed Form Lower Bound Approximating $p_{n,m,s} = n![z^n]\left(\sum_{k=0}^s\frac{z^k}{k!}\right)^m$

Here, I found $p_{n,m,s} = n![z^n]\left(\sum_{k=0}^s\frac{z^k}{k!}\right)^m = \sum\limits_{\substack{k_1 + \cdots + k_m=n\\0\leq k_i \leq s}} \frac{n!}{k_1!\cdots k_m!}$ as the number of ways to ...
An object $G$ in a category $\mathcal{C}$ is called a group object if, given any object $X$ in $\mathcal{C}$, there is a group structure on the morphisms $\operatorname{hom}\left(X,G\right)$ such that ...