2025/10/16 by Inagaki, Ryota, Pramatarova, Dimana
#05A15 #05A19 #11B50 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2510.14956
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.