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arXiv · 2607.07256

Dyck paths on colored lattices

Manjil P. Saikia
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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 $n=cm+r-1$.

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Manjil P. Saikia. 2026-07-08. Dyck paths on colored lattices. https://arxiv.org/abs/2607.07256

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