Hemjyoti Nath

activity

20242026

collaborators

11 papers

math.NT2026

Proof of a Conjecture of Cui, Gu and Tang on 18-Colored Generalized Frobenius Partitions

Hirakjyoti Das, Hemjyoti Nath, Abhishek Sarma

Recently, the study of the number of $k$ -colored generalized Frobenius partitions, denoted by $c ϕ_{k} (n)$ , has witnessed renewed interest. In this paper, we investigate congruence pr…

math.NT2026

2- and 3-Dissections of Second-, Sixth-, and Eighth-Order Mock Theta Functions

Frank Garvan, Hemjyoti Nath

In this paper, we develop a systematic method for obtaining and proving $m$ -dissections of mock theta functions. In 2014, Hickerson and Mortenson showed how to derive and prove ide…

math.NT2025

Infinite families of congruences for the second order mock theta function $B (q)$

Hemjyoti Nath, Hirakjyoti Das

The arithmetic properties of the second order mock theta function $B (q)$ , introduced by McIntosh, defined by \begin{equation*} \mathcal{B}(q) := \sum_{n \geq 0} \frac{q^n…

math.NT2025

Arithmetic properties of partition functions introduced by Pushpa and Vasuki

Hemjyoti Nath, Manjil P. Saikia

In this short note, we prove several infinite family of congruences for some restricted partitions introduced by Pushpa and Vasuki (2022) (thereby, also proving a conjecture of Das…

math.NT2025

Congruences and density results for partitions into distinct even parts

Hemjyoti Nath, Abhishek Sarma

In this paper, we consider the set of partitions $p e d (n)$ which counts the number of partitions of $n$ wherein the even parts are distinct (and the odd parts are unrestricted). Usi…

math.NT2025

New arithmetic properties for overpartitions where nonoverlined parts are $ℓ$ -regular

Hemjyoti Nath, Manjil P. Saikia, James A. Sellers

In this paper, we study the partition functions $R_{ℓ}^{*} (n)$ , which count the number of overpartitions of $n$ where the non-overlined parts are $ℓ$ -regular for a…

math.NT2024

Arithmetic properties of $k$ -tuple $ℓ$ -regular partitions

Hemjyoti Nath, Manjil P. Saikia, Abhishek Sarma

In this paper, we study arithmetic properties satisfied by the $k$ -tuple $ℓ$ -regular partitions. A $k$ -tuple of partitions $(ξ_{1}, ξ_{2}, \dots, ξ_{k})$ is said to be $ℓ$ -regular…

math.NT2024

Arithmetic of 2-regular partitions with distinct odd parts

Hemjyoti Nath

Let $p o d_{2} (n)$ denote the number of $2$ -regular partitions of $n$ with distinct odd parts (even parts are unrestricted). In this article, we obtain congruences for $p o d_{2} (n)$ mod $…

math.NT2024

Parity results of PEND partition

Hemjyoti Nath

In this paper, we consider the set of partitions $p e n d (n)$ which enumerates the number of partitions of $n$ wherein the even parts are not allowed to be distinct. Using a result of…

math.NT2024

New congruences for partitions where the even parts are distinct

Hemjyoti Nath

We denote the number of partitions of $n$ wherein the even parts are distinct (and the odd parts are unrestricted) by $p e d (n)$ . In this paper, we will use generating function manip…

math.CO2024

The pod function and its connection with other partition functions

Hemjyoti Nath

The number of partitions of $n$ wherein odd parts are distinct and even parts are unrestricted, often denoted by $p o d (n)$ . In this paper, we provide linear recurrence relations for…

Proof of a Conjecture of Cui, Gu and Tang on 18-Colored Generalized Frobenius Partitions

2- and 3-Dissections of Second-, Sixth-, and Eighth-Order Mock Theta Functions

Infinite families of congruences for the second order mock theta function B(q)

Arithmetic properties of partition functions introduced by Pushpa and Vasuki

Congruences and density results for partitions into distinct even parts

New arithmetic properties for overpartitions where nonoverlined parts are ℓ-regular

Arithmetic properties of k-tuple ℓ-regular partitions

Arithmetic of 2-regular partitions with distinct odd parts

Parity results of PEND partition

New congruences for partitions where the even parts are distinct

The pod function and its connection with other partition functions

Infinite families of congruences for the second order mock theta function $B (q)$

New arithmetic properties for overpartitions where nonoverlined parts are $ℓ$ -regular

Arithmetic properties of $k$ -tuple $ℓ$ -regular partitions