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Partition identities involving gaps and weights
Author(s):
Krishnaswami
Alladi
Journal:
Trans. Amer. Math. Soc.
349
(1997),
5001-5019.
MSC (1991):
Primary 11P83, 11P81;
Secondary 05A19
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Abstract:
We obtain interesting new identities connecting the famous partition functions of Euler, Gauss, Lebesgue, Rogers-Ramanujan and others by attaching weights to the gaps between parts. The weights are in general multiplicative. Some identities involve powers of 2 as weights and yield combinatorial information about some remarkable partition congruences modulo powers of 2.
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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/S0002-9947-97-01831-X
PII:
S 0002-9947(97)01831-X
Keywords:
Partitions,
weights,
gaps,
Durfee squares,
powers of 2
Received by editor(s):
October 10, 1995
Received by editor(s) in revised form:
June 3, 1996
Additional Notes:
Research supported in part by the National Science Foundation Grant DMS 9400191.
Copyright of article:
Copyright
1997,
American Mathematical Society
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