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Short Proof of a Conjecture by Dyson

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Classic Papers in Combinatorics

Part of the book series: Modern Birkhäuser Classics ((MBC))

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Abstract

By applying Lagrange’s interpolation formula (see, for example, Kopal4) to the function of x that is identically equal to I and then putting x = 0

Dyson made a mathematical conjecture in his work on the distribution of energy levels in complex systems. A proof is given. which is much shorter than two that have been published before.

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References

  1. F. J. Dyson, J. Math. Phys. 3, 140, 157, 166 (1962).

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  2. J. Gunson, J. Math. Phys. 3, 752 (1962).

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  3. K.. G. Wilson, J. Math. Phys. 3, 1040 (1962).

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  4. Z. Kopal, Numerical Analysis (Chapman and Hall, London, 1955), p. 21.

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Author information

Authors and Affiliations

  1. Department of Statistics, Virginia Polytechnic Institute, Blacksburg, Virginia

    I. J. Good

Authors
  1. I. J. Good
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Brandeis University, Waltham, MA, 02454, USA

    Ira Gessel

  2. Department of Mathematics, Massachusetts Institute of Technology (MIT), Cambridge, MA, 02139, USA

    Gian-Carlo Rota

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© 2009 Birkhäuser Boston, a part of Springer Science+Business Media, LLC

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Good, I.J. (2009). Short Proof of a Conjecture by Dyson. In: Gessel, I., Rota, GC. (eds) Classic Papers in Combinatorics. Modern Birkhäuser Classics. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4842-8_31

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  • DOI: https://doi.org/10.1007/978-0-8176-4842-8_31

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-0-8176-4841-1

  • Online ISBN: 978-0-8176-4842-8

  • eBook Packages: Springer Book Archive

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