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Research Article

The quantum MacMahon Master Theorem

Stavros Garoufalidis, Thang T. Q. Lê, and Doron Zeilberger
PNAS September 19, 2006 103 (38) 13928-13931; https://doi.org/10.1073/pnas.0606003103
Stavros Garoufalidis
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  • For correspondence: stavros@math.gatech.edu
Thang T. Q. Lê
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Doron Zeilberger
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  1. Edited by Robion C. Kirby, University of California, Berkeley, CA, and approved July 24, 2006 (received for review July 17, 2006)

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Abstract

We state and prove a quantum generalization of MacMahon's celebrated Master Theorem and relate it to a quantum generalization of the boson–fermion correspondence of physics.

Footnotes

  • †To whom correspondence should be addressed. E-mail: stavros{at}math.gatech.edu
  • Author contributions: S.G., T.T.Q.L., and D.Z. performed research.

  • The authors declare no conflict of interest.

  • This paper was submitted directly (Track II) to the PNAS office.

  • © 2006 by The National Academy of Sciences of the USA
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The quantum MacMahon Master Theorem
Stavros Garoufalidis, Thang T. Q. Lê, Doron Zeilberger
Proceedings of the National Academy of Sciences Sep 2006, 103 (38) 13928-13931; DOI: 10.1073/pnas.0606003103

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The quantum MacMahon Master Theorem
Stavros Garoufalidis, Thang T. Q. Lê, Doron Zeilberger
Proceedings of the National Academy of Sciences Sep 2006, 103 (38) 13928-13931; DOI: 10.1073/pnas.0606003103
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Proceedings of the National Academy of Sciences: 103 (38)
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  • Article
    • Abstract
    • MacMahon's Master Theorem
    • Quantum Algebra, Right-Quantum Matrices, and Quantum Determinants
    • A q-Version of MacMahon's Master Theorem
    • Computer Code
    • Proof
    • Some Remarks on the Boson–Fermion Correspondence
    • Acknowledgments
    • Footnotes
    • References
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