All Questions

Suppose we are given information about distributions of random permutations $\sigma, \tau : \Omega \to S_n$ as follows: $$p^1_{k,l} = \mathbb P(\sigma(k) = l), p^2_{k',l'} = \mathbb P(\tau(k) = l), p^{...

Let $m\geq 3$ be fixed and $n\to\infty$. Consider $v=(v_j)_{j\leq m}$ with $v_1,\ldots,v_m\in \{-1,+1\}^n$. Let: $N_I(v)$ be the number of sequences $u_1,\ldots,u_m\in \{-1,+1\}^n$ isometric to $v$ ...

The Cohen-Lenstra measure on the set of abelian p-groups assigns $\mathbb{P}(G) = \prod_{i \geq 1} \left( 1 - \frac{1}{p^i}\right) \cdot |\mathrm{Aut}(G)|^{-1} $. Apparently, this is equivalent to ...