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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

   

 

A simple proof of the Zeilberger-Bressoud $ q$-Dyson theorem


Authors: Gyula Károlyi and Zoltán Lóránt Nagy
Journal: Proc. Amer. Math. Soc. 142 (2014), 3007-3011
MSC (2010): Primary 05A19, 05A30, 33D05, 33D60
Published electronically: May 28, 2014
MathSciNet review: 3223356
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Abstract: As an application of the Combinatorial Nullstellensatz, we give a short polynomial proof of the $ q$-analogue of Dyson's conjecture formulated by Andrews and first proved by Zeilberger and Bressoud.


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Additional Information

Gyula Károlyi
Affiliation: School of Mathematics and Physics, The University of Queensland, Brisbane, Queensland 4072, Australia
Address at time of publication: Institute of Mathematics, Eötvös University, Pázmány P. sétány 1/c, Budapest, 1117 Hungary
Email: karolyi@cs.elte.hu

Zoltán Lóránt Nagy
Affiliation: Alfréd Rényi Institute of Mathematics, Reáltanoda utca 13–15, Budapest, 1053 Hungary
Email: nagyzoltanlorant@gmail.com

DOI: http://dx.doi.org/10.1090/S0002-9939-2014-12041-7
Keywords: Constant term identities, Laurent polynomials, Dyson's conjecture, Combinatorial Nullstellensatz
Received by editor(s): March 26, 2012
Received by editor(s) in revised form: August 16, 2012, and September 26, 2012
Published electronically: May 28, 2014
Additional Notes: This research was supported by the Australian Research Council, by ERC Advanced Research Grant No. 267165, and by Hungarian National Scientific Research Funds (OTKA) Grants 67676 and 81310
Communicated by: Jim Haglund
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.