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GENERALISATION OF KEITH’S CONJECTURE ON 9-REGULAR PARTITIONS AND 3-CORES

Part of: Additive number theory; partitions Combinatorics

Published online by Cambridge University Press:  20 May 2014

BERNARD L. S. LIN  and
ANDREW Y. Z. WANG
BERNARD L. S. LIN
Affiliation:
School of Sciences, Jimei University, Xiamen 361021, PR China email linlishuang@jmu.edu.cn
ANDREW Y. Z. WANG*
Affiliation:
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, PR China email yzwang@uestc.edu.cn
*
✉yzwang@uestc.edu.cn
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Abstract

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Recently, Keith used the theory of modular forms to study 9-regular partitions modulo 2 and 3. He obtained one infinite family of congruences modulo 3, and meanwhile proposed an analogous conjecture. In this note, we show that 9-regular partitions and 3-cores satisfy the same congruences modulo 3. Thus, we first derive several results on 3-cores, and then generalise Keith’s conjecture and get a stronger result, which implies that all of Keith’s results on congruences modulo 3 are consequences of our result.

Keywords

regular partitionscongruences3-cores

MSC classification

Secondary: 05A17: Partitions of integers 11P83: Partitions; congruences and congruential restrictions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 90 , Issue 2 , October 2014 , pp. 204 - 212
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

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