All Questions

From "Noncrossing partitions in surprising locations" by Jon McCammond: Certain mathematical structures make a habit of reoccuring in the most diverse list of settings. Some obvious ...

When trying to build a dual formulation for lattice gauge theories using Weingarten integration I am getting sums of the kind $$I^{m, n}_{\mu, \nu} (\sigma, \tau) = \sum_{\pi \in S_n} \chi_\mu (\pi \...

I am working on a certain collision problem. The probability of forming $j$ particles upon collision of $m$ and $n$ particles is given by the following equation: $$R\left(n,m,j\right)=\sum_{k=0}^{n}...

The Problem: The following question of Horst Knörrer is a sort of toy problem coming from mathematical physics. Let $x_1, x_2, \dots, x_n$ and $y_1,y_2,\dots, y_n$ be two sets of real numbers. We ...

Let $O(N)$ be the orthogonal group, and $a,b,c\in\mathbb N$. The question is: $$\int_{O(N)}U_{11}^aU_{22}^bU_{33}^cdU=?$$ This is quite a tricky question: (1) The first thought would go to ...

For a lattice in $\mathbb{R}^2$, if we include each edge independently with probability $p$ (i.e. bond percolation), it is well known that there is a critical probability $0 < p_c < 1$ depending ...