Enumeration of Generalized Dyck Paths Based on the Height of Down-Steps Modulo $k

• Published in: The Electronic journal of combinatorics Vol. 30; no. 1
• Main Authors: Heuberger, Clemens, Selkirk, Sarah J., Wagner, Stephan
• Format: Journal Article
• Language: English
• Published: 10.02.2023

For fixed non-negative integers $k$, $t$, and $n$, with $t < k$, a $k_t$-Dyck path of length $(k+1)n$ is a lattice path that starts at $(0, 0)$, ends at $((k+1)n, 0)$, stays weakly above the line $y = -t$, and consists of steps from the step-set $\{(1, 1), (1, -k)\}$. We enumerate the family of $...