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

DOI:
https://doi.org/10.1090/S0002-9947-97-01944-2

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:
https://doi.org/10.1090/S0002-9947-97-01944-2

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