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arXiv · 2608.27208

Hankel determinants of Catalan-like sequences

Shane Chern·Wenle Shi
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Abstract

In this paper, we compute the (shifted) Hankel determinants of Catalan-like sequences, which arise naturally from the weighted enumerations of nonintersecting Motzkin meanders. Among these determinant evaluations, one and a half are newly discovered, featuring generic shifted Hankel determinants; two were formulated earlier by Cigler and Krattenthaler in an equivalent combinatorial form; and the rest were conjectured by Cigler. As an application, we further confirm a conjectural binomial determinant identity proposed by Cigler and Krattenthaler.

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Shane Chern, Wenle Shi. 2026-08-27. Hankel determinants of Catalan-like sequences. https://arxiv.org/abs/2608.27208

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