Pranjal Talukdar

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20222024

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math.NT2024

Divisibility of an analogue of $t$ -core partition function by powers of primes

Pranjal Talukdar

A partition of a positive integer $n$ is said to be $t$ -core if none of its hook lengths are divisible by $t$ . Recently, two analogues, $a_{t} (n)$ and $b_{t} (n)$ ,…

math.NT2024

Arithmetic properties of an analogue of $t$ -core partitions

Pranjal Talukdar

An integer partition of a positive integer $n$ is called to be $t$ -core if none of its hook lengths are divisible by $t$ . Recently, Gireesh, Ray and Shivashankar [`A new analogue o…

math.NT2023

Ramanujan-type Congruences for Partition $k$ -Tuples with $5$ -Cores

Manjil P. Saikia, Abhishek Sarma, Pranjal Talukdar

We prove several Ramanujan-type congruences modulo powers of $5$ for partition $k$ -tuples with $5$ -cores, for $k = 2, 3, 4$ . We also prove some new infinite families of congruences m…

math.NT2022

Congruences for $k$ -elongated plane partition diamonds

Nayandeep Deka Baruah, Hirakjyoti Das, Pranjal Talukdar

In the eleventh paper in the series on MacMahons partition analysis, Andrews and Paule [1] introduced the $k$ elongated partition diamonds. Recently, they [2] revisited the topic.…

Divisibility of an analogue of t-core partition function by powers of primes

Arithmetic properties of an analogue of t-core partitions

Ramanujan-type Congruences for Partition k-Tuples with 5-Cores

Congruences for k-elongated plane partition diamonds

Divisibility of an analogue of $t$ -core partition function by powers of primes

Arithmetic properties of an analogue of $t$ -core partitions

Ramanujan-type Congruences for Partition $k$ -Tuples with $5$ -Cores

Congruences for $k$ -elongated plane partition diamonds