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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 combinatorial proof of Schur's 1926 partition theorem


Author: David M. Bressoud
Journal: Proc. Amer. Math. Soc. 79 (1980), 338-340
MSC: Primary 05A17; Secondary 10A45
MathSciNet review: 565367
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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 [Enhancements On Off] (What's this?)

  • [1] G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, 4th ed., Clarendon Press, Oxford, 1960.
  • [2] 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

DOI: http://dx.doi.org/10.1090/S0002-9939-1980-0565367-X
PII: S 0002-9939(1980)0565367-X
Article copyright: © Copyright 1980 American Mathematical Society