3 problems

Let $A$ and $B$ be arch systems, each with $n$ arches. Let $\operatorname{Av}(A)$ and $\operatorname{Av}(B)$ be their avoidance classes, and let their enumeration sequences count o…

For each positive integer $n$, let ${{\mathcal M}}_n$ denote the main cohort of arch systems with $n$ arches, and let a cohort be an equivalence class under $\sim$. Main-cohort max…

Let arch systems be Catalan structures, and let $A\sim B$ denote the equivalence relation generated by the four intrinsic rules defined in the paper. For an arch system $A$, let…