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ARITHMETIC PROPERTIES OF $(k,\ell )$-REGULAR BIPARTITIONS

Part of: Additive number theory; partitions Combinatorics

Published online by Cambridge University Press:  01 December 2016

LIUQUAN WANG
LIUQUAN WANG*
Affiliation:
Department of Mathematics, National University of Singapore, Singapore, 119076 email wangliuquan@u.nus.edu, mathlqwang@163.com
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Abstract

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Let $B_{k,\ell }(n)$ denote the number of $(k,\ell )$-regular bipartitions of $n$. Employing both the theory of modular forms and some elementary methods, we systematically study the arithmetic properties of $B_{3,\ell }(n)$ and $B_{5,\ell }(n)$. In particular, we confirm all the conjectures proposed by Dou [‘Congruences for (3,11)-regular bipartitions modulo 11’, Ramanujan J.40, 535–540].

Keywords

partitions; congruences(k, ℓ)-regular bipartitionsmodular forms

MSC classification

Primary: 05A17: Partitions of integers
Secondary: 11P83: Partitions; congruences and congruential restrictions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 95 , Issue 3 , June 2017 , pp. 353 - 364
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

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