A combinatorial correspondence related to Göllnitz' (big) partition theorem and applications
Author:
Krishnaswami Alladi
Journal:
Trans. Amer. Math. Soc. 349 (1997), 27212735
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/S0002994797019442
PII:
S 00029947(97)019442
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
