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

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.

46 pages

References in corpus (4)

• A simple approach to some Hankel determinants
• q-Chebyshev polynomials
• Some elementary observations on Narayana polynomials and related topics II: q-Narayana polynomials
• A theorem on shifted Hankel determinants

Cited by in corpus (1)

• A theorem on shifted Hankel determinants