# Tagged Questions

24 views

### Combinatorial proof of Rothe-Hagen

Wikipediate states the Rothe-Hagen identity below generalizes Vandermonde convolution: ...
44 views

### Burnside's Lemma and Stirling Numbers of the First Kind

I've seen that $n!=\displaystyle\sum_{p=0}^n s(n, p)n^p$, where $s(n, p)$ are the signed Stirling Numbers of the First Kind, whose absolute values count the number of permutations in $S_n$ which have ...
58 views

### The anti-symmetrization and simetrization operators are mutually orthogonal

For each vector $x=(x_1,\dots,x_n)$ of an $n$-dimensional vector space $V$, and for each permutation $s$ of the symmetric group on the $n$-element set $S_n$, put $s(x)=(x_{s(1)},\dots,x_{s(n)})$. Then ...
What finite Graphs $G$ have the property that for all $v,w\in G$, there is exactly one automorphism $\phi$ of $G$ with $\phi(v)=w$? Of course, each of the three graphs with one or two vertices have ...
Recall that a graph $G$ is arc transitive if the natural action of $\mathrm{Aut}(G)$ on $A(G) = \{ (u,v) | \{u,v\} \in E(G)\}$ is transitive. In other words, given $(u,v),(u'.v') \in A(G)$ one finds ...