scholarly journals On 3-divisibility of 9- and 27-regular partitions

2021 ◽  
Author(s):  
Sarma Abinash
Keyword(s):  
Regular Partitions

Congruences for 7 and 49-regular partitions modulo powers of 7

2017 ◽  
Vol 46 (3) ◽  
pp. 821-833 ◽  
Author(s):  
Chandrashekar Adiga ◽  
Ranganatha Dasappa
Keyword(s):  
Regular Partitions

scholarly journals Generating functions and congruences for 9-regular and 27-regular partitions in 3 colours

2022 ◽  
Vol Volume 44 - Special... ◽  
Author(s):  
Nayandeep Deka Baruah ◽  
Hirakjyoti Das
Keyword(s):  
Generating Functions ◽  
Regular Partitions ◽  
Positive Integers

Let $b_{\ell;3}(n)$ denote the number of $\ell$-regular partitions of $n$ in 3 colours. In this paper, we find some general generating functions and new infinite families of congruences modulo arbitrary powers of $3$ when $\ell\in\{9,27\}$. For instance, for positive integers $n$ and $k$, we have\begin{align*}b_{9;3}\left(3^k\cdot n+3^k-1\right)&\equiv0~\left(\textup{mod}~3^{2k}\right),\\b_{27;3}\left(3^{2k+3}\cdot n+\dfrac{3^{2k+4}-13}{4}\right)&\equiv0~\left(\textup{mod}~3^{2k+5}\right).\end{align*}

Parity results for 11-, 13- and 17-regular partitions

2018 ◽  
Vol 151 (1) ◽  
pp. 97-109
Author(s):  
Tao Yan Zhao ◽  
Jing Jin ◽  
Olivia X. M. Yao
Keyword(s):  
Regular Partitions
Sign in / Sign up

Export Citation Format

Share Document