4 problems

Let $a_t^{\star}(n)$ denote the number of hooks of length $t$ among all self-conjugate partitions of $n$. For integers $n\geq0$ and $m\geq1$, define divisibility in the usual sense…

For positive integers $s$ and $k$, a partition is a self-conjugate $(s,s+1,\ldots,s+k)$-core partition if it is equal to its conjugate and is simultaneously an $s$-core, an $(s+1)$…

Weighted self-conjugate core-average conjecture.

Congruences for $[...]$.