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INFINITE FAMILIES OF CONGRUENCES MODULO 3 AND 9 FOR BIPARTITIONS WITH 3-CORES

Part of: Additive number theory; partitions Combinatorics

Published online by Cambridge University Press:  27 August 2014

OLIVIA X. M. YAO
OLIVIA X. M. YAO*
Affiliation:
Department of Mathematics, Jiangsu University, Jiangsu, Zhenjiang 212013, PR China email [email protected]
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Abstract

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Let $A_{3}(n)$ denote the number of bipartitions of $n$ with 3-cores. Recently, Lin [‘Some results on bipartitions with 3-core’, J. Number Theory139 (2014), 44–52] established some congruences modulo 4, 5, 7 and 8 for $A_{3}(n)$. In this paper, we prove several infinite families of congruences modulo 3 and 9 for $A_{3}(n)$ by employing two identities due to Ramanujan.

Keywords

bipartitionst-corescongruences

MSC classification

Primary: 11P83: Partitions; congruences and congruential restrictions
Secondary: 05A17: Partitions of integers
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 91 , Issue 1 , February 2015 , pp. 47 - 52
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

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