3 problems

Let $v(n)$ count odd-balanced unimodal sequences of size $2n+2$, and let $v(m,n)$ count those with rank $m$. Let $\ell\not\equiv-1\pmod8$ be prime and let $k$ be a positive integer…

Bryson–Ono–Pitman–Rhoades conjecture. For all $n$,

Let $u(m,n)$ denote the number of strongly unimodal sequences of size $n$ and rank $m$. Strict log-concavity conjecture. For $n\ge37$ and $|m|\le n-23$, we have … The conjecture is…