scholarly journals Modular forms and $k$-colored generalized Frobenius partitions

2018 ◽  
Vol 371 (3) ◽  
pp. 2159-2205 ◽  
Author(s):  
Heng Huat Chan ◽  
Liuquan Wang ◽  
Yifan Yang
Keyword(s):  
Modular Forms ◽  
Generalized Frobenius Partitions ◽  
Frobenius Partitions

CONGRUENCES MODULO 5 AND 7 FOR 4-COLORED GENERALIZED FROBENIUS PARTITIONS

2016 ◽  
Vol 103 (2) ◽  
pp. 157-176 ◽  
Author(s):  
HENG HUAT CHAN ◽  
LIUQUAN WANG ◽  
YIFAN YANG
Keyword(s):  
Modular Forms ◽  
Generalized Frobenius Partitions ◽  
Frobenius Partitions

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

scholarly journals Congruences for generalized Frobenius partitions with 4 colors

2011 ◽  
Vol 311 (17) ◽  
pp. 1892-1902 ◽  
Author(s):  
Nayandeep Deka Baruah ◽  
Bipul Kumar Sarmah
Keyword(s):  
Generalized Frobenius Partitions ◽  
Frobenius Partitions

Congruences modulo powers of 2 for generalized Frobenius partitions with six colors

2019 ◽  
Vol 15 (06) ◽  
pp. 1173-1181
Author(s):  
Su-Ping Cui ◽  
Nancy S. S. Gu
Keyword(s):  
Powers Of 2 ◽  
Generalized Frobenius Partitions ◽  
Frobenius Partitions

A generalized Frobenius partition of [Formula: see text] with [Formula: see text] colors is a two-rowed array [Formula: see text] where [Formula: see text], and the integer entries are taken from [Formula: see text] distinct copies of the non-negative integers distinguished by color, and the rows are ordered first by size and then by color with no two consecutive like entries in any row. Let [Formula: see text] denote the number of this kind of partitions of [Formula: see text] with [Formula: see text] colors. In this paper, we establish some congruences modulo powers of 2 for [Formula: see text].

NEW RAMANUJAN TYPE CONGRUENCE MODULO 7 FOR 4-COLORED GENERALIZED FROBENIUS PARTITIONS

2014 ◽  
Vol 10 (03) ◽  
pp. 637-639 ◽  
Author(s):  
BERNARD L. S. LIN
Keyword(s):  
Congruence Modulo ◽  
Generalized Frobenius Partitions ◽  
Frobenius Partitions

In this brief note, we prove one unexpected Ramanujan type congruence modulo 7 for the number cϕ4(n) of generalized Frobenius partitions of n with four colors.

scholarly journals Congruences involving generalized Frobenius partitions

1993 ◽  
Vol 16 (2) ◽  
pp. 413-415 ◽  
Author(s):  
James Sellers
Keyword(s):  
Cyclic Permutation ◽  
Generalized Frobenius Partitions ◽  
Frobenius Partitions

The goal of this paper is to discuss congruences involving the functioncϕm¯(n), which denotes the number of generalized Frobenius partitions ofnwithmcolors whose order ismunder cyclic permutation of themcolors.

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