Partition identities involving gaps and weights
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- by Krishnaswami Alladi PDF
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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.References
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Additional Information
- Krishnaswami Alladi
- Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611
- MR Author ID: 24845
- Email: alladi@math.ufl.edu
- 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 1997 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 349 (1997), 5001-5019
- MSC (1991): Primary 11P83, 11P81; Secondary 05A19
- DOI: https://doi.org/10.1090/S0002-9947-97-01831-X
- MathSciNet review: 1401759