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Differences of Partition Functions: The Anti-telescoping Method

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Book cover From Fourier Analysis and Number Theory to Radon Transforms and Geometry

Part of the book series: Developments in Mathematics ((DEVM,volume 28))

Abstract

The late Leon Ehrenpreis originally posed the problem of showing that the difference of the two Rogers–Ramanujan products had positive coefficients without invoking the Rogers–Ramanujan identities. We first solve the problem generalized to the partial products and subsequently solve several related problems. The object is to introduce the anti-telescoping method which is capable of wide generalization.

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References

  1. G. E. Andrews, An analytic proof of the Rogers-Ramanujan-Gordon identities, Amer. J. Math., 88 (1966), 844–846.

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  2. G. E. Andrews A generalization of the Göllnitz-Gordon partition theorems, Proc. Amer. Math. Soc., 18 (1967), 945–952.

    MATH  MathSciNet  Google Scholar 

  3. G. E. Andrews, Applications of basic hypergeometric functinos, SIAM Review, 16 (1974), 441–484.

    Article  MATH  MathSciNet  Google Scholar 

  4. G. E. Andrews and R. J. Baxter, A motivated proof of the Rogers-Ramanujan identities, Amer. Math. Monthly, 96 (1989), 401–409.

    Article  MATH  MathSciNet  Google Scholar 

  5. G. E. Andrews and K. Eriksson, Integer Partitions, Cambridge University Press, Cambridge, 2004.

    Book  MATH  Google Scholar 

  6. A. Berkovich and F. Garvan, Dissecting the Stanley partition function, J. Comb. Th. (A), 112 (2005), 277–291.

    Article  MATH  MathSciNet  Google Scholar 

  7. H. Göllnitz, Partitionen mit Differenzenbedingungen, J. reine u. angew. Math., 225 (1965), 154–190.

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  8. B. Gordon, A combinatorial generalization of the Rogers-Ramanujan identities, Amer. J. Math., 83 (1961), 393–399.

    Article  MATH  MathSciNet  Google Scholar 

  9. K. W. J. Kadell, An injection for the Ehrenpreis Rogers-Ramanujan problem, J. Comb. Th. (A), 86 (1999), 390–394.

    Article  MATH  MathSciNet  Google Scholar 

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Acknowledgements

Partially supported by National Science Foundation Grant DMS-0801184

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Authors and Affiliations

  1. Department of Mathematics, The Pennsylvania State University, University Park, PA, 16802, USA

    George E. Andrews

Authors
  1. George E. Andrews
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Correspondence to George E. Andrews .

Editor information

Editors and Affiliations

  1. , Einstein Institute of Mathematics, Hebrew University of Jerusalem, Jerusalem, 91904, Israel

    Hershel M. Farkas

  2. , Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, 08544, New Jersey, USA

    Robert C. Gunning

  3. , Department of Mathematics, Temple University, Wachman Hall 608, Philadelphia, 19122, Pennsylvania, USA

    Marvin I. Knopp

  4. , Department of Mathematics, University of Michigan, Church St. 530, Ann Arbor, 48109, Michigan, USA

    B. A. Taylor

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Dedicated to the memory of the great Leon Ehrenpreis.

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Andrews, G.E. (2013). Differences of Partition Functions: The Anti-telescoping Method. In: Farkas, H., Gunning, R., Knopp, M., Taylor, B. (eds) From Fourier Analysis and Number Theory to Radon Transforms and Geometry. Developments in Mathematics, vol 28. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4075-8_1

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