3 problems

Let $\delta$ be a rooted weakly increasing range map and let $n\geqslant 0$. Write $\mathsf{Cl}_\delta(n)$ for the corresponding set of $\delta$-cliffs, ordered by $\preccurlyeq'$.…

Let $FS_{s,t}$ be the set of $t$-Fuss–Catalan paths of semilength $s$, and let $FC_{s,t}$ denote the same path set. Let $\operatorname{istat}$ be a statistic on these paths, and le…

Let $m,n$ be positive integers, let $h$ be the Coxeter number in type $\widetilde{C}_n$, and consider the Fuß–Catalan case $b=mh+1$. Let ${\sf core}(\widetilde{C}_n,mh+1)$ denote t…