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Related papers: Congruences for Restricted Plane Overpartitions Mo…

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In this paper, we generalize recent work of Mizuhara, Sellers, and Swisher that gives a method for establishing restricted plane partition congruences based on a bounded number of calculations. Using periodicity for partition functions, our…

Number Theory · Mathematics 2017-04-14 Ali H. Al-Saedi

In this article, we first investigate the partitions whose parts are congruent to $a$ or $b$ modulo $k$ with the aid of separable integer partition classes with modulus $k$ introduced by Andrews. Then, we introduce the…

Combinatorics · Mathematics 2024-07-01 Thomas Y. He , C. S. Huang , H. X. Li , X. Zhang

Recently, Drema and Saikia (2023) proved several congruences modulo powers of 2 and 3 for overpartition triples with odd parts. We extend their list substantially. We prove several congruences modulo powers of 2 for overpartition k-tuples…

Number Theory · Mathematics 2024-08-23 Manjil P. Saikia , Abhishek Sarma , James A. Sellers

Recently there has been quite a bit of study carried out related to arithmetic properties of overpartitions into non-multiples of two co-prime integers. The paper [19] by Nadji et al. looked into congruences modulo $3$ and powers of $2$ for…

Number Theory · Mathematics 2025-05-01 Suparno Ghoshal , Arijit Jana

Inspired by the recent work by Nadji, Ahmia and Ram\'irez, we examined the arithmetic properties of $\bar{B}_{l_1,l_2} (n)$, the number of overpartitions of n whose parts are neither divisible by $l_1$ nor divisible by $l_2$. In particular,…

Number Theory · Mathematics 2025-07-04 Anakha V

In a recent work, Andrews defined the singular overpartitions with the goal of presenting an overpartition analogue to the theorems of Rogers--Ramanujan type for ordinary partitions with restricted successive ranks. As a small part of his…

Combinatorics · Mathematics 2017-12-27 Doris D. M. Sang , Diane Y. H. Shi

Let $\overline{p}_{k}(n)$ denote the number of overpartition $k$-tuples of $n$. In 2023, Saikia \cite{saikia} conjectured the following congruences: \begin{align*} \overline{p}_{q}(8n+2)& \equiv 0 \pmod{4},\quad \overline{p}_{q}(8n+3)\equiv…

Number Theory · Mathematics 2025-09-23 G. Kavya Keerthana , S. Ananya , Ranganatha D

Generating functions for plane overpartitions are obtained using various methods such as nonintersecting paths, RSK type algorithms and symmetric functions. We extend some of the generating functions to cylindric partitions. Also, we show…

Combinatorics · Mathematics 2010-09-17 Sylvie Corteel , Cyrille Savelief , Mirjana Vuletić

In this short note, we prove several new congruences for the overcubic partition triples function, using both elementary techniques and the theory of modular forms. These extend the recent list of such congruences given by Nayaka,…

Number Theory · Mathematics 2025-09-10 Manjil P. Saikia , Abhishek Sarma

In this paper, we establish two new Ramanujan-type congruences for the overpartition function: $\overline{p}(11\times(8n+5))\equiv 0 \pmod{11}$ and $\overline{p}(13\times 2^6(8n+7))\equiv 0 \pmod{13}$. The proofs rely on the theory of…

Number Theory · Mathematics 2026-03-10 XuanLing Wei

The primary focus of this paper is overpartitions, a type of partition that plays a significant role in $q$-series theory. In 2006, Treneer discovered an explicit infinite family of congruences of overpartitions modulo $5$. In our research,…

Number Theory · Mathematics 2023-09-04 Qi-Yang Zheng

In a recent paper, Jin, Liu, and Xia \cite{JLX} presented some modulo 4 congruences for $\overline{spt2}(n)$, the number of smallest parts in the overpartitions of $n$ where the smallest part is even and is not overlined. In this paper, we…

Number Theory · Mathematics 2025-10-27 Robson da Silva

Recently, Shen (2016) and Alanazi et al. (2016) studied the arithmetic properties of the $\ell$-regular overpartition function $\overline{A}_\ell (n)$, which counts the number of overpartitions of $n$ into parts not divisible by $\ell$. In…

Number Theory · Mathematics 2017-06-12 Shane Chern

We define $\overline{R_l^*}(n)$ as the number of overpartitions of $n$ in which non-overlined parts are not divisible by $l$. In a recent work, Nath, Saikia, and the second author established several families of congruences for…

Number Theory · Mathematics 2025-08-07 Bishnu Paudel , James A. Sellers , Haiyang Wang

We investigate Ramanujan congruences for the function which counts the overpartitions of n with restricted odd differences. In particular, we show that only one such congruence exists. Our method involves using the theory of modular forms…

Number Theory · Mathematics 2022-04-07 Michael Hanson , Jeremiah Smith

Recently, Alanazi, Munagi, and Saikia employed the theory of modular forms to investigate the arithmetic properties of the function $\overline{R_{\ell,\mu}}(n)$, which enumerates the overpartitions of $n$ where no part is divisible by…

Number Theory · Mathematics 2025-05-29 Bishnu Paudel , James A. Sellers , Haiyang Wang

We present a study of three families of Kronecker coefficients, which we describe in terms of reduced Kronecker coefficients. This study is grounded on the generating function of the coefficients, proved by a bijection between two…

Combinatorics · Mathematics 2016-04-05 L. Colmenarejo

Recently, Drema and N. Saikia (2023) and M. P. Saikia, Sarma, and Sellers (2023) proved several congruences modulo powers of $2$ for overpartition triples with odd parts. In this paper, we study further divisibility properties of…

Number Theory · Mathematics 2026-04-29 Hirakjyoti Das , Manjil P. Saikia , Abhishek Sarma

Recently, Nadji, Ahmia and Ram\'{i}rez \cite{Nadji2025} investigate the arithmetic properties of ${\bar B}_{\ell_1,\ell_2}(n)$, the number of overpartitions where no part is divisible by $\ell_1$ or $\ell_2$ with $\gcd(\ell_1,\ell_2)$$=1$…

Number Theory · Mathematics 2025-08-06 N. K. Meher

Ramanujan's celebrated congruences of the partition function $p(n)$ have inspired a vast amount of results on various partition functions. Kwong's work on periodicity of rational polynomial functions yields a general theorem used to…

Number Theory · Mathematics 2024-05-31 Matthew S. Mizuhara , James A. Sellers , Holly Swisher
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