An unexpected Ramanujan-type congruence modulo 7 for 4-colored generalized Frobenius partitions

Zhang, Wenlong; Wang, Chun

doi:10.1007/s11139-015-9770-0

Cited by 10 publications

(3 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where we denote For more results on k-colored generalized Frobenius partitions, see [2,3], [5]- [22], [24]- [26].…”

Section: Introductionmentioning

confidence: 99%

Congruences Modulo Powers of 3 for 3- and 9-Colored Generalized Frobenius Partitions

Wang¹

2018

Preprint

View full text Add to dashboard Cite

Let cφ k (n) be the number of k-colored generalized Frobenius partitions of n. We establish some infinite families of congruences for cφ3(n) and cφ9(n) modulo arbitrary powers of 3, which refine the results of Kolitsch. For example, for k ≥ 3 and n ≥ 0, we prove thatWe give two different proofs to the congruences satisfied by cφ9(n). One of the proofs uses an relation between cφ9(n) and cφ3(n) due to Kolitsch, for which we provide a new proof in this paper.

show abstract

“…where we denote For more results on k-colored generalized Frobenius partitions, see [2,3], [5]- [22], [24]- [26].…”

Section: Introductionmentioning

confidence: 99%

Congruences Modulo Powers of 3 for 3- and 9-Colored Generalized Frobenius Partitions

Wang¹

2018

Preprint

View full text Add to dashboard Cite

show abstract

“…We remark here that there is no analogue of Ramanujan's congruence for = 5 even though (1.2) holds. Recently, Zhang and Wang [20] proved (1.5) using the quintuple-product identity and a new identity involving the generating function for cφ 4 (n) (instead of cφ 4 (2n)).…”

Section: Introductionmentioning

confidence: 99%

Congruences Modulo 5 and 7 for 4-Colored Generalized Frobenius Partitions

Chan¹,

Wang²,

Yang³

2016

J. Aust. Math. Soc.

View full text Add to dashboard Cite

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 $c\unicode[STIX]{x1D719}_{4}(10n+6)\equiv 0\;\text{mod}\;5$.

show abstract

“…The representation (6.2) was first deduced by W. Zhang and C. Wang [43] from (6.1), where they used it to give an elementary proof of the congruence cφ 4 (7n + 5) ≡ 0 (mod 7). 6.2.…”

mentioning

confidence: 99%