3 problems

Catalan-polynomial structure conjecture. There exists a unique power series $P(x)$ with non-negative integer coefficients such that every $V_i(z)$ is the product of $C(z)$ and a po…

Centered gamma moment-generating-function conjecture. For every $n$, $k$, and $P$,

Let $X$ have a non-degenerate non-normal distribution with existing moment generating function, and let $T_{n,\gamma}$ denote the test statistic defined in the paper for sample siz…