Article contents
CONGRUENCES MODULO 5 AND 7 FOR 4-COLORED GENERALIZED FROBENIUS PARTITIONS
Published online by Cambridge University Press: 21 December 2016
Abstract
Let $c\unicode[STIX]{x1D719}_{k}(n)$ denote the number of
$k$-colored generalized Frobenius partitions of
$n$. Recently, new Ramanujan-type congruences associated with
$c\unicode[STIX]{x1D719}_{4}(n)$ were discovered. In this article, we discuss two approaches in proving such congruences using the theory of modular forms. Our methods allow us to prove congruences such as
$c\unicode[STIX]{x1D719}_{4}(14n+6)\equiv 0\;\text{mod}\;7$ and Seller’s congruence
$c\unicode[STIX]{x1D719}_{4}(10n+6)\equiv 0\;\text{mod}\;5$.
MSC classification
- Type
- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 103 , Issue 2 , October 2017 , pp. 157 - 176
- Copyright
- © 2016 Australian Mathematical Publishing Association Inc.
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