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 (7)

• A simple approach to some Hankel determinants
• q-Chebyshev polynomials
• A theorem on shifted Hankel determinants
• Some elementary observations on Narayana polynomials and related topics II: q-Narayana polynomials
• A curious class of Hankel determinants
• Hankel determinants of harmonic numbers and related topics
• The Hessenberg matrices and Catalan and its generalized numbers

Cited by in corpus (4)

• A theorem on shifted Hankel determinants
• Some remarks on generalized Fibonacci and Lucas polynomials
• Shifted Hankel determinants of Catalan numbers and related results
• The explicit formula of Hankel determinant with Catalan elements