Proof of the Somos-4 Hankel Determinants Conjecture

2007/12/06 by Guoce Xin, Xin, Guoce
Mathematics · #15A15 #30B70 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Mathematical functions and polynomials #math.CO #msc:15A15 #msc:30B70

paper · pdf · doi:10.48550/arxiv.0712.0933

3 pages

arxiv created 2007/12/06 · openalex publication_date 2007/12/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By considering the fundamental equation x=y-y²=z-z³, Somos conjectured that the Hankel determinants for the generating series y(z) are the Somos-4 numbers. We prove this conjecture by using the quadratic transformation for Hankel determinants of Sulanke and Xin.

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