5 problems

Monotonicity conjecture. For $n\ge 5$, the ratio

Limiting-ratio conjecture.

Asymptotic partition-proportion conjecture.

Monotonicity conjecture. The ratio $g_f(2n)/g(2n)$ is monotonously decreasing when $n\geq 5$.

Let $G^{'}(N,n)$ be the set of graphical partitions of $N$ into at most $n$ parts as defined in the paper, and let $I_e(n)$ be the corresponding index set of admissible even values…