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Catalan numbers, Hankel determinants and Fibonacci polynomials

2018/01/17 by Johann Cigler, Cigler, Johann · 1 citation
Mathematics · Physics and Astronomy · #05A19 #11B39 #15B36 #33C45 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1801.05608

openalex publication_date 2018/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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