Year: 2026
Type: preprint
Abstract: Fried recently enumerated Dyck paths having equally many black and white cells below them, for the chessboard coloring (Narayana numbers) and the column-alternating coloring (Fuss--Catalan numbers). We prove a generalization here: for the coloring of columns modulo any $c\ge2$, the number of Dyck paths of semilength $n$ whose $c$ residue classes carry equal weight is the Raney number $\Raney_{c+1,r}(m)$, where $n=cm+r-1$.
Source: arXiv (Cornell University)
Author: Saikia, Manjil P.
Institution: Ahmedabad University
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7167808948
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