5 problems

Let $S_{n,d}$ be the complete split graph, and let $\mathsf{SortedRec}(S_{n,d})$ be the set of sorted recurrent configurations on $S_{n,d}$. For a configuration $c$, write…

Let $S_{n,d}$ be the complete split graph, let $\mathfrak{F}_{n,d}^{CTI}(q,t)$ be the $q,t$-CTI polynomial, and let $\mathsf{Schr\ddot{o}der}_{n,d}$ be the set of $(n,d)$-Schröder…

Let $S_{n,d}$ be the complete split graph, and let $\mathfrak{F}_{n,d}^{CTI}(q,t)$ and $\mathfrak{F}_{n,d}^{ITC}(q,t)$ denote the $q,t$-CTI and $q,t$-ITC polynomials, respectively.…

Wilmes' multiplicity conjecture. If there are exactly $l$ distinct partitions $\Pi_j\in\operatorname{\mathcal{P}}_{k+1}$ such that

Square non-zero configuration conjecture. The cardinality satisfies