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.

**[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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DOI:
http://dx.doi.org/10.1090/S0002-9939-1980-0565367-X

Article copyright:
© Copyright 1980
American Mathematical Society