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A combinatorial correspondence related to Göllnitz' (big) partition theorem and applications
Author(s):
Krishnaswami
Alladi
Journal:
Trans. Amer. Math. Soc.
349
(1997),
2721-2735.
MSC (1991):
Primary 05A17, 05A19;
Secondary 11P83
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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.
References:
- 1.
- K. Alladi, Partition identities involving gaps and weights, Trans. Amer. Math. Soc. (to appear).
- 2.
- K. Alladi, and G. E. Andrews, A new key identity for Göllnitz' (big) partition theorem in Proc. 10
 Anniv. Conf. Ramanujan Math. Soc., Contemp. Math. (to appear). - 3.
- K. Alladi, G. E. Andrews and B. Gordon, Generalizations and refinements of a partition theorem of Göllnitz, J. Reine Angew. Math. 460 (1995), 165-188. MR 96c:11119
- 4.
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- 5.
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- 6.
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 Series: Their Development and Applications in Analysis, Number Theory, Combinatorics, Physics and Computer Algebra, CBMS Regional Conf. Ser. in Math., 66 AMS, Providence, 1986. MR 88b:11063 - 8.
- D. M. Bressoud, A combinatorial proof of Schur's 1926 partition theorem, Proc. Amer. Math. Soc., 79 (1980), 333-340. MR 81f:05017
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- 11.
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Additional Information:
Krishnaswami
Alladi
Affiliation:
Department of Mathematics, University of Florida, Gainesville, Florida 32611
Email:
alladi@math.ufl.edu
DOI:
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.
Copyright of article:
Copyright
1997,
American Mathematical Society
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