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Transactions of the American Mathematical Society

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Partition identities involving gaps and weights

Author: Krishnaswami Alladi
Journal: Trans. Amer. Math. Soc. 349 (1997), 5001-5019
MSC (1991): Primary 11P83, 11P81; Secondary 05A19
MathSciNet review: 1401759
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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

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.
Article copyright: © Copyright 1997 American Mathematical Society