New Ramanujan-like congruences modulo powers of 2 and 3 for overpartitions

OXM Yao, EXW Xia - Journal of Number Theory, 2013 - Elsevier
Let p¯(n) denote the number of overpartitions of n. In recent works, Fortin, Jacob and
Mathieu, and Hirschhorn and Sellers established some congruences modulo powers of 2 for …

Congruences modulo 9 and 27 for overpartitions

EXW Xia - The Ramanujan Journal, 2017 - Springer
Let ̄ p (n) p¯(n) denote the number of overpartitions of n. Fortin et al. and Hirschhorn and
Sellers established some congruences modulo powers of 2 for ̄ p (n) p¯(n). Recently, Xia …

[HTML][HTML] Ramanujan type identities and congruences for partition pairs

PC Toh - Discrete Mathematics, 2012 - Elsevier
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[HTML][HTML] Ramanujan-type congruences for overpartitions modulo 5

WYC Chen, LH Sun, RH Wang, L Zhang - Journal of Number Theory, 2015 - Elsevier
Let p¯(n) denote the number of overpartitions of n. In this paper, we show that p¯(5 n)≡(− 1)
np¯(4⋅ 5 n)(mod 5) for n≥ 0 and p¯(n)≡(− 1) np¯(4 n)(mod 8) for n≥ 0 by using the …

[HTML][HTML] Overpartition pairs modulo powers of 2

B Kim - Discrete Mathematics, 2011 - Elsevier
An overpartition of n is a non-increasing sequence of positive integers whose sum is n in
which the first occurrence of a number may be overlined. In this article, we investigate the …

Arithmetic properties of bipartitions with even parts distinct

BLS Lin - The Ramanujan Journal, 2014 - Springer
In this work, we consider various arithmetic properties of the function ped− 2 (n) that denotes
the number of bipartitions of n with even parts distinct. We prove two infinite families of …

Arithmetic properties of overpartition pairs

WYC Chen, BLS Lin - arXiv preprint arXiv:1009.5016, 2010 - arxiv.org
Bringmann and Lovejoy introduced a rank for overpartition pairs and investigated its role in
congruence properties of $\bar {pp}(n) $, the number of overpartition pairs of n. In particular …

New Ramanujan type congruences modulo 5 for overpartitions

DQJ Dou, BLS Lin - The Ramanujan Journal, 2017 - Springer
Let p¯(n) denote the number of overpartitions of n. In this paper, we shall show that for n≥ 0,
p¯(80 n+ r)≡ 0 (mod 5), where r= 8, 52, 68, and 72. In addition, we present a short …

The pod function and its connection with other partition function

H Nath - Rad Hrvatske akademije znanosti i umjetnosti …, 2025 - hrcak.srce.hr
THE POD FUNCTION AND ITS CONNECTION WITH OTHER PARTITION FUNCTIONS
Hemjyoti Nath 1. Introduction A partition of a positive integ Page 1 RAD HAZU. MATEMATIČKE …

[HTML][HTML] Quadratic forms and congruences for ℓ-regular partitions modulo 3, 5 and 7

QH Hou, LH Sun, L Zhang - Advances in Applied Mathematics, 2015 - Elsevier
Let b ℓ (n) be the number of ℓ-regular partitions of n. We show that the generating functions
of b ℓ (n) with ℓ= 3, 5, 6, 7 and 10 are congruent to the products of two items of Ramanujan's …