Add to ORKGGeorge Andrews and Peter Paule have recently conjectured an infinite family of congruences modulo powers of 3 for the 2-elongated plane partition function $d_2(n)$. This congruence family appears difficult to prove by classical methods. We prove a refined form of this conjecture by expressing the associated generating functions as elements of a ring of modular functions isomorphic to a localization of $\mathbb{Z}[X]$.Comment: 31 pages, 2 figures, 3 tables. References a Mathematica supplement which can be found online at <https://www.risc.jku.at/people/nsmoot/2eplanepartsupplement.nb
AbstractThe goal of this paper is to prove new congruences involving 2-colored and 3-colored general...
In this paper, we establish infinite families of congruences in consecutive arithmetic progressions ...
The ordinary partition function p(n) counts the number of representations of a positive integer n as...
In 2021 da Silva, Hirschhorn, and Sellers studied a wide variety of congruences for the $k$-elongate...
The arithmetic properties of the ordinary partition function p(n) have been the topic of intensive s...
Let $PD_{2, 3}(n)$ count the number of partitions of $n$ with designated summands in which parts ar...
In this work we introduce new combinatorial objects called $d$--fold partition diamonds, which gener...
We prove that if a prime ℓ>3 divides pk−1, where p is prime, then there is a congruence modulo ℓ, li...
AbstractThe partition function P(n) satisfy some congruence properties. Eichhorn and Ono prove the e...
The arithmetic properties of the ordinary partition function $p(n)$ have been the topic of intensive...
Recently, Lin introduced two new partition functions PD$_t(n)$ and PDO$_t(n)$, which count the total...
In this article we exhibit new explicit families of congruences for the overpartition function, maki...
AbstractAlthough much is known about the partition function, little is known about its parity. For t...
We study general properties of the dessins d’enfants associated with the Hecke congruence subgroups ...
Recently, Andrews, Dixit and Yee introduced partition functions associated with Ramanujan/Watson thi...
AbstractThe goal of this paper is to prove new congruences involving 2-colored and 3-colored general...
In this paper, we establish infinite families of congruences in consecutive arithmetic progressions ...
The ordinary partition function p(n) counts the number of representations of a positive integer n as...
In 2021 da Silva, Hirschhorn, and Sellers studied a wide variety of congruences for the $k$-elongate...
The arithmetic properties of the ordinary partition function p(n) have been the topic of intensive s...
Let $PD_{2, 3}(n)$ count the number of partitions of $n$ with designated summands in which parts ar...
In this work we introduce new combinatorial objects called $d$--fold partition diamonds, which gener...
We prove that if a prime ℓ>3 divides pk−1, where p is prime, then there is a congruence modulo ℓ, li...
AbstractThe partition function P(n) satisfy some congruence properties. Eichhorn and Ono prove the e...
The arithmetic properties of the ordinary partition function $p(n)$ have been the topic of intensive...
Recently, Lin introduced two new partition functions PD$_t(n)$ and PDO$_t(n)$, which count the total...
In this article we exhibit new explicit families of congruences for the overpartition function, maki...
AbstractAlthough much is known about the partition function, little is known about its parity. For t...
We study general properties of the dessins d’enfants associated with the Hecke congruence subgroups ...
Recently, Andrews, Dixit and Yee introduced partition functions associated with Ramanujan/Watson thi...
AbstractThe goal of this paper is to prove new congruences involving 2-colored and 3-colored general...
In this paper, we establish infinite families of congruences in consecutive arithmetic progressions ...
The ordinary partition function p(n) counts the number of representations of a positive integer n as...