All Questions

We consider a set $E$ with an involution (having perhaps fixed points). We denote orbits by $\lbrace x,\overline{x}\rbrace$ (with $\overline{x}=x$ in the case of a fixed point). We consider sequences $...

Let $\pi$ be a permutation in $S_n$ with cycle type $\lambda$. How many factorizations into two factors $\pi=\sigma_1\sigma_2$ are there, such that the subgroup $\langle \sigma_1,\sigma_2\rangle$ ...

If you have $m$ sequences $a_{11},\dots,a_{1n_1}$ through $a_{m1},\dots,a_{mn_m}$ each sorted in ascending order (assume there are no duplicates) then there is an unique way to merge them. How many ...