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My Association and Collaboration with George Andrews

Torchbearer of Ramanujan and Partitions

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Lattice Path Combinatorics and Applications

Part of the book series: Developments in Mathematics ((DEVM,volume 58))

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Abstract

These are personal reflections on my association, and a report of my collaboration, with George Andrews given at the International Conference on Lattice Path Combinatorics and Applications, California Polytechnic University, Pomona.

Section 2 on personal recollections is based on the speech given at the banquet, while Sect. 3 on collaboration is based on a talk in one of the technical sessions of the conference.

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References

  1. Alladi, K.: A combinatorial correspondence related to Göllnitz’ (Big) partition theorem. Trans. Am. Math. Soc. 349, 2721–2735 (1997)

    Article  Google Scholar 

  2. Alladi, K.: On a partition theorem of Göllnitz and quartic transformations (with an appendix by Gordon, B.). J. Number Theory 69, 153–180 (1998)

    Article  MathSciNet  Google Scholar 

  3. Alladi, K., Andrews, G.E.: A new key identity for Göllnitz’ (Big) partition theorem. In: Proceedings of the 10th Anniversary Conference of Ramanujan Mathematical Society. Contemporary Mathematics, vol. 210, pp. 229–241 (1997)

    Google Scholar 

  4. Alladi, K., Andrews, G.E.: A quartic key identity for a partition theorem of Göllnitz. J. Number Theory 75, 220–236 (1999)

    Article  MathSciNet  Google Scholar 

  5. Alladi, K., Andrews, G.E.: The dual of Göllnitz’ (Big) partition theorem. Ramanujan J. 36, 171–202 (2015)

    Article  MathSciNet  Google Scholar 

  6. Alladi, K., Gordon, B.: Generalizations of Schur’s partition theorem. Manuscripta Math. 79, 113–126 (1993)

    Article  MathSciNet  Google Scholar 

  7. Alladi, K., Andrews, G.E., Berkovich, A.: A new four parameter \(q\)-series identity and its partition implications. Invent. Math. 153, 231–260 (2003)

    Article  MathSciNet  Google Scholar 

  8. Alladi, K., Andrews, G.E., Gordon, B.: Generalizations and refinements of a partition theorem of Göllnitz. J. Reine Angew. Math. 460, 165–188 (1995)

    MathSciNet  MATH  Google Scholar 

  9. Alladi, K., Andrews, G.E., Gordon, B.: Refinements and generalizations of Capparelli’s conjecture on partitions. J. Algebr. 174, 1591–1608 (1995)

    Article  MathSciNet  Google Scholar 

  10. Andrews, G.E.: On Schur’s second partition theorem. Glas. Math. J. 19, 127–132 (1967)

    Article  MathSciNet  Google Scholar 

  11. Andrews, G.E.: A new generalization of Schur’s second partition theorem. Acta Arith. 14, 429–434 (1968)

    Article  MathSciNet  Google Scholar 

  12. Andrews, G.E.: A general partition theorem with difference conditions. Am. J. Math. 91, 18–24 (1969)

    Article  Google Scholar 

  13. Andrews, G.E.: On a partition theorem of Göllnitz and related formulae. J. Reine Angew. Math. 236, 37–42 (1969)

    MathSciNet  MATH  Google Scholar 

  14. Andrews, G.E.: The Theory of Partitions. Encyclopedia of Mathemathics, vol. 2. Addison–Wesley, Reading (1976)

    Google Scholar 

  15. Andrews, G.E.: \(q\)-Series: Their Development and Application in Analysis, Number Theory, Combinatorics, Physics and Computer Algebra. NSF-CBMS Lectures, vol. 66. American Mathematical Society, Providence (1985)

    Google Scholar 

  16. Andrews, G.E.: Schur’s theorem, Capparelli’s conjecture and the \(q\)-trinomial coefficients. In: Proceedings of the Rademacher Centenary Conference 1992. Contemporary Mathematics, vol. 166, pp. 141–154 (1994)

    Google Scholar 

  17. Capparelli, S.: On some representations of twisted affine Lie algebras and combinatorial identities. J. Algebr. 154, 335–355 (1993)

    Article  MathSciNet  Google Scholar 

  18. Göllnitz, H.: Partitionen mit Differenzenbedingungen. J. Reine Angew. Math. 225, 154–190 (1967)

    MathSciNet  MATH  Google Scholar 

  19. Lepowsky, J., Wilson, R.L.: A Lie-theoretic interpretation and proof of the Rogers–Ramanujan identities. Adv. Math. 145, 21–72 (1982)

    Article  MathSciNet  Google Scholar 

  20. Lepowsky, J., Wilson, R.L.: The structure of standard modules I, universal algebras and the Rogers–Ramanujan identities. Invent. Math. 77, 199–290 (1984)

    Article  MathSciNet  Google Scholar 

  21. Ramanujan, S.: The Lost Notebook and Unpublished Papers. Springer, New Delhi (1987)

    MATH  Google Scholar 

  22. Schur, I.: Zur Additiven Zahlentheorie. In: Gesammelte Abhandlungen, vol. 2, pp. 43–70. Springer, Berlin (1937)

    Google Scholar 

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Acknowledgements

I thank the organizers of the Conference on Lattice Paths Combinatorics, especially Alan Krinik, not only to have invited me to speak in a technical session, but also to have given me the role as Banquet Speaker. I am also grateful to Christian Krattenthaler for a very careful reading of the manuscript and for help with the Latex file of this paper.

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Authors and Affiliations

  1. Department of Mathematics, University of Florida, Gainesville, FL, 32611, USA

    Krishnaswami Alladi

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  1. Krishnaswami Alladi
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Correspondence to Krishnaswami Alladi .

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Editors and Affiliations

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

    George E. Andrews

  2. Fakultät für Mathematik, Universität Wien, Vienna, Austria

    Christian Krattenthaler

  3. Department of Mathematics and Statistics, California State Polytechnic University, Pomona, Pomona, CA, USA

    Alan Krinik

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Alladi, K. (2019). My Association and Collaboration with George Andrews. In: Andrews, G., Krattenthaler, C., Krinik, A. (eds) Lattice Path Combinatorics and Applications. Developments in Mathematics, vol 58. Springer, Cham. https://doi.org/10.1007/978-3-030-11102-1_4

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