4 problems

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 $m,n,k$ be nonnegative integers. Write $\nabla$, $\Theta_{e_k}$, and $\Delta_{h_m}$ for the nabla, Theta, and Delta operators on symmetric functions, let $\omega$ be the standa…

For nonnegative integers $a,b,c$, let $N_{a,b,c}$ denote the number of 20V configurations on the rectangular grid of size $(a+b+1)\times(b+c+1)$ with DWBC4-type boundary conditions…

Ascent conjecture. The number of Schröder paths $p\in R_{n-1}$ with $k-1$ ascents is equal to the number of inversion sequences $e\in\mathbf{I}_n(021)$ with $k$ distinct values.