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A polynomial identity implying Schur's partition theorem


Author: Ali Kemal Uncu
Journal: Proc. Amer. Math. Soc. 148 (2020), 3307-3324
MSC (2010): Primary 05A15, 05A17, 05A19, 11B37, 11P83
DOI: https://doi.org/10.1090/proc/14991
Published electronically: March 23, 2020
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Abstract: We propose and prove a new polynomial identity that implies Schur's partition theorem. We give combinatorial interpretations of some of our expressions in the spirit of Kurşungöz. We also present some related polynomial and $ q$-series identities.


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Additional Information

Ali Kemal Uncu
Affiliation: Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Linz, Altenbergerstrasse 69A, 4040 Linz, Austria
Email: akuncu@risc.jku.at

DOI: https://doi.org/10.1090/proc/14991
Keywords: Schur's partition theorem, integer partitions, $q$-trinomial coefficients, $q$-series
Received by editor(s): March 4, 2019
Received by editor(s) in revised form: September 17, 2019, December 20, 2019, and December 27, 2019
Published electronically: March 23, 2020
Additional Notes: Research of the author was supported by the Austrian Science Fund FWF, SFB50-07, -09, and -11 Projects.
Communicated by: Amanda Folsom
Article copyright: © Copyright 2020 American Mathematical Society