MathOverflow

I am trying to prove a complex identity involving harmonic numbers $H_n$ and generalized harmonic numbers $H^{(2)}_n$.
For integers $m, a, b, c$ such that $c \ge 0$ and $c \le \min\left(\lfloor \frac{2m-b-1}{2} \rfloor, m-a-1\right)$, let us define the weight term:$$ W_k = \frac{(-1)^{3m-a-b+k}}{(2m-b-1-2k)! (m-a-k-1)! (k!)^3} $$...

Qiaochu Yuan recently tweeted the following analogy:
the sense in which prime numbers are the building blocks of other numbers (wrt multiplication) is exactly analogous to the sense in which connected graphs are the building blocks of arbitrary graphs. an arbitrary graph, not necessarily connected, consists...

In CatDat we are currently working out the proof that $\mathbf{Rel}$ has quotients of congruences. Apparently this cannot be deduced from general results, for example $\mathbf{Rel}$ does not have reflexive coequalizers. Daniel Schepler has found a proof...

My advisor and I are doing a project on spectral geometry. To get the necessary prerequisites down, I am consulting Alberto Arabia's Introduction to Isospectrality. Theorem 1.2.2 in this book reads as follows:
Let $\mathbf M$ be a PLB-surface. Let $(G,\Gamma_1,\Gamma_2)$ be a Gassman triple where $G$ is a finite subgroup of $\operatorname{Iso}(\mathbf M)$ and where the subgroups $\Gamma_i$ act freely on $\mathbf M$. Then, the quotients $\mathbf M_i:=\Gamma...