Manjil P. Saikia

activity

20122026

most citedParity biases in partitions and restricted partitions

10 citations · 51 across the 41 of their papers we have counts for

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27 papers · 1 filter

math.NT2026

Congruences for the Andrews--Uncu partition function $EO_{u} (n)$

Nayandeep Deka Baruah, Hirakjyoti Das, Manjil P. Saikia +1

In 2018, Andrews defined and studied the partition function $EO (n)$ , which counts the number of partitions of $n$ where each even part is less than each odd part. Thereaf…

math.NT2026

On the positivity of truncated pentagonal number series and some conjectures of Merca

Manjil P. Saikia, Abhishek Sarma

Let $ν_{2} (m)$ denote the $2$ -adic valuation of a positive integer $m$ and set $N_{m} = m (1 + ν_{2} (m) /2)$ . We prove four conjectures of Merca on the nonnegativity of truncated pen…

math.NT2026

Generalized Frobenius Partitions Modulo Powers of $2$

Manjil P. Saikia

Let $c ϕ_{k} (n)$ denote the number of $k$ -colored generalized Frobenius partitions of $n$ . We prove that, for every $m \geq 2$ and every $k \equiv 2 (mod 2^{m})$ , \[ \sum_{n\geq0}cϕ_k(n)q^n…

math.NT2026

Internal congruences modulo powers of 2 for $k$ -colored overpartitions into odd parts

Manjil P. Saikia, Prabal Talukdar, Dazhao Tang

Let $p o_{k} (n)$ denote the number of $k$ -colored overpartitions of $n$ into odd parts. For every odd number of colors, we establish infinite families of internal congruenc…

math.NT2026

Extending Recent Arithmetic Properties of Overcubic Partition Tuples

Saikat Maity, Manjil P. Saikia

In recent years, several mathematicians have looked at a class of partitions called the overcubic partition $k$ -tuples, for small values of $k$ . They have proved several divisibili…

math.NT2026

Some Comments on Regular Overpartitions modulo $2^{k}$

Abdulaziz M. Alanazi, Manjil P. Saikia

For coprime integers $ℓ, μ \geq 2$ , Alanazi, Munagi, and Saikia (2026) studied $R_{ℓ, μ} (n)$ , the number of overpartitions of $n$ in which no part is divisible by $\el…

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

Arithmetic Properties of Generalized Cubic and Overcubic Partitions

Hirakjyoti Das, Saikat Maity, Manjil P. Saikia

We prove several congruences satisfied by the generalized cubic and generalized overcubic partition functions, recently introduced by Amdeberhan, Sellers, and Singh. We also prove…

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

Some Properties of Overpartitions into Nonmultiples of Two Integers

Abdulaziz M. Alanazi, Augustine O. Munagi, Manjil P. Saikia

We consider properties of overpartitions that are simultaneously {\ell}-regular and μ-regular, where {\ell} and μ are positive relatively prime integers. We prove a seven-way combi…

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★ 5 cited

Further Arithmetic Properties of Overcubic Partition Triples

Manjil P. Saikia, Abhishek Sarma

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 th…

math.NT2024

Arithmetic Properties modulo powers of $2$ and $3$ for Overpartition $k$ -Tuples with Odd Parts

Hirakjyoti Das, Manjil P. Saikia, Abhishek Sarma

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 p…

math.NT2023

Arithmetic properties modulo powers of $2$ for overpartition $k$ -tuples with odd parts

Manjil P. Saikia, Abhishek Sarma, James A. Sellers

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…

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.NT2023★ 5 cited

Some Missed Congruences modulo powers of $2$ for $t$ -colored overpartitions

Manjil P. Saikia

Recently, Nayaka and Naika (2022) proved several congruences modulo $16$ and $32$ for $t$ -colored overpartitions with $t = 5, 7, 11$ and $13$ . We extend their list using an algorithmic…

math.NT2023★ 1 cited

Biases in Non-Unitary Partitions

Pankaj Jyoti Mahanta, Manjil P. Saikia, Abhishek Sarma

Recently, the concept of parity bias in integer partitions has been studied by several authors. We continue this study here, but for non-unitary partitions (namely, partitions with…

math.NT2020★ 6 cited

Some properties of Zumkeller numbers and $k$ -layered numbers

Pankaj Jyoti Mahanta, Manjil P. Saikia, Daniel Yaqubi

Generalizing the concept of a perfect number is a Zumkeller or integer perfect number that was introduced by Zumkeller in 2003. The positive integer $n$ is a Zumkeller number if it…

math.NT2019★ 2 cited

On Deficient Perfect Numbers with Four Distinct Prime Factors

Parama Dutta, Manjil P. Saikia

For a positive integer $n$ , if $σ (n)$ denotes the sum of the positive divisors of $n$ , then $n$ is called a deficient perfect number if $σ (n) = 2 n - d$ for some positive divisor $d$ of…

math.NT2016

Some Results on Generalized Multiplicative Perfect Numbers

Alexandre Laugier, Manjil P. Saikia, Upam Sarmah

In this article, based on ideas and results by J. Sándor (2001, 2004), we define $k$ -multiplicatively $e$ -perfect numbers and $k$ -multiplicatively $e$ -superperfect numbers and prov…

math.NT2013

Some results about Linear Recurrence Relation Homomorphisms

Alexandre Laugier, Manjil P. Saikia

In this paper we propose a definition of a recurrence relation homomorphism and illustrate our definition with a few examples. We then define the period of a k-th order of linear r…

math.NT2013★ 2 cited

A new proof of Lucas' Theorem

Alexandre Laugier, Manjil P. Saikia

We give a new proof of Lucas' Theorem in elementary number theory.

math.NT2012

Binomial Symbols and Prime Moduli

Manjil P. Saikia, Jure Vogrinc

We try to improve a problem asked in an Indian Math Olympiad. We give a brief overview of the work done in Saikia and Vogrinc (2011) and Saikia and Vogrinc where the authors have f…

math.NT2012

Some Properties of Fibonacci Numbers, Generalized Fibonacci Numbers and Generalized Fibonacci Polynomial Sequences

Alexandre Laugier, Manjil P. Saikia

In this paper we study the Fibonacci numbers and derive some interesting properties and recurrence relations. We prove some charecterizations for $F_{p}$ , where $p$ is a prime of a c…

Congruences for the Andrews--Uncu partition function EOu​(n)

On the positivity of truncated pentagonal number series and some conjectures of Merca

Generalized Frobenius Partitions Modulo Powers of 2

Internal congruences modulo powers of 2 for k-colored overpartitions into odd parts

Extending Recent Arithmetic Properties of Overcubic Partition Tuples

Some Comments on Regular Overpartitions modulo 2k

Arithmetic properties of partition functions introduced by Pushpa and Vasuki

Arithmetic Properties of Generalized Cubic and Overcubic Partitions

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

Some Properties of Overpartitions into Nonmultiples of Two Integers

Arithmetic properties of k-tuple ℓ-regular partitions

Further Arithmetic Properties of Overcubic Partition Triples

Arithmetic Properties modulo powers of 2 and 3 for Overpartition k-Tuples with Odd Parts

Arithmetic properties modulo powers of 2 for overpartition k-tuples with odd parts

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

Some Missed Congruences modulo powers of 2 for t-colored overpartitions

Biases in Non-Unitary Partitions

Some properties of Zumkeller numbers and k-layered numbers

On Deficient Perfect Numbers with Four Distinct Prime Factors

Some Results on Generalized Multiplicative Perfect Numbers

Some results about Linear Recurrence Relation Homomorphisms

A new proof of Lucas' Theorem

Binomial Symbols and Prime Moduli

Some Properties of Fibonacci Numbers, Generalized Fibonacci Numbers and Generalized Fibonacci Polynomial Sequences

Congruences for the Andrews--Uncu partition function $EO_{u} (n)$

Generalized Frobenius Partitions Modulo Powers of $2$

Internal congruences modulo powers of 2 for $k$ -colored overpartitions into odd parts

Some Comments on Regular Overpartitions modulo $2^{k}$

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

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

Arithmetic Properties modulo powers of $2$ and $3$ for Overpartition $k$ -Tuples with Odd Parts

Arithmetic properties modulo powers of $2$ for overpartition $k$ -tuples with odd parts

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

Some Missed Congruences modulo powers of $2$ for $t$ -colored overpartitions

Some properties of Zumkeller numbers and $k$ -layered numbers