3 problems

Let $q(n)$ denote the number of partitions of $n$ into distinct parts. A sequence is log-concave when $q(n)^2\geq q(n-1)q(n+1)$, and the third-order Turán inequalities are the corr…

Dong–Ji's conjecture. For the sequence $a_n=q(n)$, one has $A>0$ for $n\geq230$, $B>0$ for $n\geq272$, and $I>0$ for $n\geq267$. The source records that the first two thresholds we…

The quartic-invariant conjecture for $q(n)$. The following inequalities hold: