Proof of the Somos-4 Hankel Determinants Conjecture

Guoce Xin

Proof of the Somos-4 Hankel Determinants Conjecture

Combinatorics 2007-12-07 v1

Authors: Guoce Xin

Abstract

By considering the fundamental equation $x=y-y^2=z-z^3$ , 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.

Cite

@article{arxiv.0712.0933,
  title  = {Proof of the Somos-4 Hankel Determinants Conjecture},
  author = {Guoce Xin},
  journal= {arXiv preprint arXiv:0712.0933},
  year   = {2007}
}

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3 pages

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