4 problems

Let $d$ be a positive integer, and let $\Lambda$ be a collection of $k\geq 3$ nontrivial partitions of $d$. The collection satisfies the Riemann-Hurwitz condition when it satisfies…

Zieve's realizability conjecture. The branch datum $B$ is realizable provided that

The prime-degree realizability conjecture. Every compatible branch datum is realizable whenever its degree $d$ is a prime number.

Let $n$ be a positive integer, and let $\leq\ell<k\leq n$. Define … … … These parameters give the first family of admissible triples of square identities. Optimality conjecture. Th…