4 problems

Let $B(k,\mu)=\sum_i {k\brace i}\mu^i$ denote the Bell polynomial, and write $B_x=B(x,1)$. For a Poisson random variable with mean $\mu$, its $k$th raw moment is $B(k,\mu)$. Bell-n…

Generalized Bell-polynomial relation. The relation

Let $p$ be a fixed positive integer. Let $u_1=1$, let $u_2,\dots,u_p$ and $d_1,\dots,d_p$ be variables, and let $F_1=1$ and $F_i=F_i(\{u_k\},\{d_k\})$ for $i=2,\dots,p$ be the uniq…

Let $S$ be the surface, $\mathscr{L}$ the line bundle, and $Y=|\mathscr{L}|$ of dimension $N$. Let $f$ be the relevant map, let $M_i(S,\mathscr{L})$ be the classes defined by … let…