4 problems

Let $u$ and $v$ be Ballot paths of lengths $L$ and $L+1$, respectively. Let $v^*$ be the Anchored Cross path of length $L$ obtained by right reduction of $v$, with heights defined…

Conjecture 8. The source introduces these paths as the configurations used to formulate the subsequent orbit-sum relations, but the supplied candidate span contains only the setup…

Let $u$ and $v$ be Dyck paths of lengths $L$ and $L+1$, respectively. Let $^*v$ be the Ballot path of length $L$ obtained by left reduction of $v$, so that … Let ${\cal O}_l(w,s)$…

For each positive integer $k$, let $D'_{k,u,n}$ denote the number of $k$-dimensional balanced ballot paths of length parameter $n$ having semisymmetric height $u$, and consider the…