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THE 7-REGULAR AND 13-REGULAR PARTITION FUNCTIONS MODULO 3
Published online by Cambridge University Press: 11 January 2016
Abstract
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
MSC classification
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- Research Article
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- © 2016 Australian Mathematical Publishing Association Inc.
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