Skeletal generalizations of Dyck paths, parking functions, and chip-firing games

Spencer Backman, Cole Charbonneau, Nicholas A. Loehr +3

For $0\le k\le n-1$, we introduce a family of $k$-skeletal paths which are counted by the $n$-th Catalan number for each $k$, and specialize to Dyck paths when $k=n-1$. We simila…