9 problems

Let $G(q)$ be the $q$-series … and let $e(n)$ and $o(n)$ denote respectively the numbers of partitions of $n$ into odd parts whose index is even and odd. Coll–Mayers–Mayers conject…

Let $\mathfrak{g}$ be a Frobenius maximal parabolic type-A seaweed, meaning a Frobenius seaweed subalgebra of $\mathfrak{sl}(n)$ obtained from a maximal parabolic construction. Its…

Recursive spectrum conjecture. The distinct eigenvalues in the spectrum of $\mathfrak{g}_{k,r}$ are precisely the integers in $[-k+1,k]$, and $\mathfrak{g}_{k,r}$ has the log-conca…

Parity-dependent spectrum conjecture. The seaweed $\mathfrak{g}$ is Frobenius, and the set of distinct eigenvalues in its spectrum is the collection of integers in

Let $p=(\lambda_1,\ldots,\lambda_l)$ be a partition of $n$ into odd parts, and let $\operatorname{ind}_S(p)$ denote its associated seaweed-index statistic. Parity conjecture. The i…

Let $C_{4,4}(n,k)$ be the composition-counting function. Red-cell recurrence conjecture. … This conjecturally describes the red cells in Table 4; no proof or resolution is supplied…

Let $C_{2,t}(n,k)$ be the composition-counting function. First-diagonal conjecture. If $t$ is even, then … for integers $t>2$ and $s\geq 0$. This describes one of the first nonzero…

Let $C_{p,q}(n,k)$ denote the composition-counting function studied in the paper. Vanishing conjecture. … for integers $s,p,k\geq 0$ with $k=2^p$. The values of $n_{k,4}$ suggest t…

Let $A$ be any top or bottom block in a Frobenius seaweed of $\mathfrak{sl}(n)$ with $n\geq 2$. For each eigenvalue $i$, let $d_i$ be its multiplicity in the multiset of eigenvalue…