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

DOI:
https://doi.org/10.1090/S0002-9947-97-01831-X

MathSciNet review:
1401759

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9947-97-01831-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.

Article copyright:
© Copyright 1997
American Mathematical Society