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THE 7-REGULAR AND 13-REGULAR PARTITION FUNCTIONS MODULO 3

Part of: Additive number theory; partitions

Published online by Cambridge University Press:  11 January 2016

ERIC BOLL  and
DAVID PENNISTON
ERIC BOLL*
Affiliation:
c/o Department of Mathematics, University of Wisconsin Oshkosh, Oshkosh, WI 54901-8631, USA email [email protected]
DAVID PENNISTON
Affiliation:
Department of Mathematics, University of Wisconsin Oshkosh, Oshkosh, WI 54901-8631, USA email [email protected]
*
✉[email protected]
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Abstract

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Let $b_{\ell }(n)$ denote the number of $\ell$-regular partitions of $n$. In this paper we establish a formula for $b_{13}(3n+1)$ modulo $3$ and use this to find exact criteria for the $3$-divisibility of $b_{13}(3n+1)$ and $b_{13}(3n)$. We also give analogous criteria for $b_{7}(3n)$ and $b_{7}(3n+2)$.

Keywords

partitionscongruencesmodular forms

MSC classification

Primary: 11P83: Partitions; congruences and congruential restrictions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 93 , Issue 3 , June 2016 , pp. 410 - 419
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

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