Catalan numbers, Hankel determinants and Fibonacci polynomials
Combinatorics
2018-04-10 v3 Classical Analysis and ODEs
Abstract
This (partly expository) paper originated from the study of Hankel determinants of convolution powers of Catalan numbers and of Narayana polynomials. This led to some Hankel determinants of signed Catalan numbers whose values are multiples of Fibonacci numbers and to some Hankel determinants of signed central binomial coefficients whose values are multiples of Lucas numbers. Most proofs are computational but we also include a combinatorial one due to Christian Krattenthaler. Finally we formulate some conjectures.
Keywords
Cite
@article{arxiv.1801.05608,
title = {Catalan numbers, Hankel determinants and Fibonacci polynomials},
author = {Johann Cigler},
journal= {arXiv preprint arXiv:1801.05608},
year = {2018}
}
Comments
31 pages, 2 figures