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q-Series and Partitions pp 45–55Cite as

In the Land of OZ

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Part of the book series: The IMA Volumes in Mathematics and Its Applications ((IMA,volume 18))

Abstract

This paper presents a proof and investigation of a curious identity which is implicit in work of K. O’Hara [7] and which was extracted and first explicitly stated by D. Zeilberger [8].

Partially supported by the National Science Foundation, the National Security Administration, and the Institute for Mathematics and its Applications.

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References

  1. G.E. Andrews, The Theory of Partitions, Addison-Wesley, 1976.

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  2. G.E. Andrews & R.J. Baxter, Lattice gas generalizations of the hard hexagon model: III, J. Stat. Physics, 47 (1987), 297–330.

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  3. D.M. Bressoud, Lattice paths and the Rogers-Ramanujan identities, preprint.

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  4. D.M. Bressoud, Unimodality of Gaussian polynomials, preprint.

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  5. W.H. Bürge, A correspondence between partitions related to generalizations of the Rogers-Ramanujan identities, Discrete Math., 34 (1981), 9–15.

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  6. W.H. Bürge, A, A three-way correspondence between partitions, Europ. J. Combinatorics, 3 (1982), 195–213.

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  7. K.M. O’hara, Unimodality of Gaussian coefficients: a constructive proof, J. Comb. Th. A, to appear.

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  8. D. Zeilberger, A one-line high school algebra proof of the unimodality of the Gaussian polynomials for [ nk ] < 20, in Dennis Stanton (ed.), q-Series and Partitions, IMA Volumes in Mathematics and its Applications, Springer-Verlag, New York (1989).

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Author information

Authors and Affiliations

  1. The Pennsylvania State University, University Park, PA, 16802, USA

    David M. Bressoud

Authors
  1. David M. Bressoud
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Editor information

Editors and Affiliations

  1. School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    Dennis Stanton

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© 1989 Springer-Verlag New York Inc.

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Bressoud, D.M. (1989). In the Land of OZ. In: Stanton, D. (eds) q-Series and Partitions. The IMA Volumes in Mathematics and Its Applications, vol 18. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-0637-5_4

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  • DOI: https://doi.org/10.1007/978-1-4684-0637-5_4

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4684-0639-9

  • Online ISBN: 978-1-4684-0637-5

  • eBook Packages: Springer Book Archive

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