Some observations about determinants which are connected with Catalan numbers and related topics
Johann Cigler

TL;DR
This paper explores matrices with determinants equal to Catalan numbers, providing new proofs, generalizations, q-analogues, and connections to Hankel determinants, along with conjectures for future research.
Contribution
It introduces new methods and generalizations related to determinants connected with Catalan numbers, including q-analogues and Hankel determinant connections.
Findings
Matrices with Catalan number determinants analyzed
New proofs and generalizations presented
Connections to Hankel determinants and conjectures proposed
Abstract
In this (mostly expository) paper I want to share some observations prompted by a class of matrices whose determinants are Catalan numbers. Considering different methods of proof we obtain some generalizations and q-analogues and connections with Hankel determinants. Finally we state some conjectures.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Mathematical Theories and Applications · Advanced Mathematical Identities
