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CONGRUENCES MODULO 2 FOR CERTAIN PARTITION FUNCTIONS

Part of: Combinatorics Additive number theory; partitions

Published online by Cambridge University Press:  11 November 2015

M. S. MAHADEVA NAIKA ,
B. HEMANTHKUMAR  and
H. S. SUMANTH BHARADWAJ
M. S. MAHADEVA NAIKA*
Affiliation:
Department of Mathematics, Bangalore University, Central College Campus, Bengaluru-560 001, Karnataka, India email [email protected]
B. HEMANTHKUMAR
Affiliation:
Department of Mathematics, Bangalore University, Central College Campus, Bengaluru-560 001, Karnataka, India email [email protected]
H. S. SUMANTH BHARADWAJ
Affiliation:
Department of Mathematics, Bangalore University, Central College Campus, Bengaluru-560 001, Karnataka, India email [email protected]
*
✉[email protected]
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Abstract

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Let $b_{3,5}(n)$ denote the number of partitions of $n$ into parts that are not multiples of 3 or 5. We establish several infinite families of congruences modulo 2 for $b_{3,5}(n)$. In the process, we also prove numerous parity results for broken 7-diamond partitions.

Keywords

congruencepartitiontheta function

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 93 , Issue 3 , June 2016 , pp. 400 - 409
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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