3 problems

Let $\overline{OPT}_k(n)$ denote the number of overpartition $k$-tuples of $n$ with odd parts. The four-congruence conjecture. For all $i\geq 1$, $n\geq 0$, and odd $r>0$, … These…

Let $\overline{p}_{q}(n)$ denote the number of overpartition $q$-tuples of $n$, where $q$ is prime. Saikia's conjecture. For all $n\geq 0$ and primes $q$, … These congruences exten…

2-adic shift conjecture. There is a 2-adic integer $\rho$ satisfying