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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A combinatorial proof of Schur’s 1926 partition theorem
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by David M. Bressoud PDF
Proc. Amer. Math. Soc. 79 (1980), 338-340 Request permission

Abstract:

One of the partition theorems published by I. J. Schur in 1926 is an extension of the Rogers-Ramanujan identities to partitions with minimal difference three. This theorem of Schur is proved here by establishing a one-to-one correspondence between the two types of partitions counted.
References
    G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, 4th ed., Clarendon Press, Oxford, 1960. I. J. Schur, Zur additiven Zahlentheorie, S.-B. Preuss. Akad. Wiss. Phys.-Math. K1., 1926, pp. 488-495. (Reprinted in I. Schur, Gesammelte Abhandlungen, vol. 3, Springer, Berlin, 1973, pp. 43-50.)
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 79 (1980), 338-340
  • MSC: Primary 05A17; Secondary 10A45
  • DOI: https://doi.org/10.1090/S0002-9939-1980-0565367-X
  • MathSciNet review: 565367