Congruences for generalized Frobenius partitions with 6 colors

Su-Ping Cui; Nancy S. S. Gu

doi:10.1216/rmj.2022.52.877

Abstract

We establish the generating function for $\overline {c\varphi _6 } (n)$ , the number of generalized Frobenius partitions of $n$ with $6$ colors whose order is $6$ under cyclic permutation of the $6$ colors. Furthermore, we find some congruences for $\overline {c\varphi _6 } (n)$ modulo $24$ .

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Su-Ping Cui. Nancy S. S. Gu. "Congruences for generalized Frobenius partitions with $6$ colors." Rocky Mountain J. Math. 52 (3) 877 - 885, June 2022. https://doi.org/10.1216/rmj.2022.52.877

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Received: 10 May 2021; Revised: 27 September 2021; Accepted: 10 October 2021; Published: June 2022

First available in Project Euclid: 16 June 2022

MathSciNet: MR4441102

zbMATH: 07556044

Digital Object Identifier: 10.1216/rmj.2022.52.877

Subjects:

Primary: 11P83

Secondary: 05A17

Keywords: congruences , generalized Frobenius partitions , integer matrix exact covering system , Ramanujan’s theta functions

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