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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A combinatorial correspondence related to Göllnitz' (big) partition theorem and applications


Author: Krishnaswami Alladi
Journal: Trans. Amer. Math. Soc. 349 (1997), 2721-2735
MSC (1991): Primary 05A17, 05A19; Secondary 11P83
MathSciNet review: 1422593
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Abstract: In recent work, Alladi, Andrews and Gordon discovered a key identity which captures several fundamental theorems in partition theory. In this paper we construct a combinatorial bijection which explains this key identity. This immediately leads to a better understanding of a deep theorem of Göllnitz, as well as Jacobi's triple product identity and Schur's partition theorem.


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Additional Information

Krishnaswami Alladi
Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611
Email: alladi@math.ufl.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-97-01944-2
PII: S 0002-9947(97)01944-2
Keywords: Partitions, G\"{o}llnitz' theorem, distinct parts, weighted words, Sylvester's identity, sliding operation
Received by editor(s): September 1, 1995
Additional Notes: Research supported in part by National Science Foundation grant DMS 9400191.
Article copyright: © Copyright 1997 American Mathematical Society