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arXiv · 2510.14956

On Weighted and Bounded Multidimensional Catalan Numbers

Ryota Inagaki·Dimana Pramatarova
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Abstract

We define a weighted analog for the multidimensional Catalan numbers, obtain matrix-based recurrences for some of them, and give conditions under which they are periodic. Building on this framework, we introduce two new sequences of triangular arrays: the first one enumerates the $k$-dimensional Balanced ballot paths of exact height $s$; the second one is a new multidimensional generalization of the Narayana numbers, which count the number of Balanced ballot paths with exactly $p$ peaks.

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Ryota Inagaki, Dimana Pramatarova. 2025-10-16. On Weighted and Bounded Multidimensional Catalan Numbers. https://arxiv.org/abs/2510.14956

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