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

collaborators

48 papers

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.CO2026

Dyck paths on colored lattices

Manjil P. Saikia

Fried recently enumerated Dyck paths having equally many black and white cells below them, for the chessboard coloring (Narayana numbers) and the column-alternating coloring (Fuss-…

math.CO2026

Hook Length Biases in $t$ -Core Partitions

Nayandeep Deka Baruah, Hirakjyoti Das, Pankaj Jyoti Mahanta +1

Recently, the theory of hook length biases has emerged as a prominent research topic. Led by Ballantine, Burson, Craig, Folsom, and Wen [\textit{Res. Math. Sci.}, 2023], hook lengt…

cs.LG2026

QEDBENCH: Quantifying the Alignment Gap in Automated Evaluation of University-Level Mathematical Proofs

Santiago Gonzalez, Alireza Amiri Bavandpour, Peter Ye +48

As Large Language Models (LLMs) saturate elementary benchmarks, the research frontier has shifted from generation to the reliability of automated evaluation. We demonstrate that st…

math.CO2026

Hook-Length Biases in $t$ -regular partitions

Manjil P. Saikia, Prabal Talukdar

Recently, there has been a lot of work on combinatorial inequalities related to hook-lengths in $t$ -regular partitions. In this short note, we give a proof using generating functio…

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.CO2025

Arithmetic properties of $t$ -Schur overpartitions

Mohammed L. Nadji, Manjil P. Saikia, James A. Sellers

In a recent work, Nadji and Ahmia introduced the $t$ -Schur overpartitions as an overpartition analogue for $t$ -Schur partitions, which generalizes the classical Schur's partitions…

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.CO2024

Symmetric Domino Tilings of Aztec Diamonds

Pravakar Paul, Manjil P. Saikia

In this paper, we give inductive sum formulas to calculate the number of diagonally symmetric, and diagonally \& anti-diagonally symmetric domino tilings of Aztec Diamonds. As a by…

math.CO2024

Combinatorial Proofs of Some Results of Andrews and El Bachraoui

Pankaj Jyoti Mahanta, Manjil P. Saikia

Recently, Andrews and El Bachraoui (2024) proved three very interesting $q$ -series identities, from which three simple looking identities involving certain restricted partitions in…

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.CO2024

A Novel Approach to Counting Perfect Matchings of Graphs

Pravakar Paul, Manjil P. Saikia

We build a new perspective to count perfect matchings of a given graph. This idea is motivated by a construction on the relative cohomology group of surfaces. As an application of…

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…

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

Dyck paths on colored lattices

Hook Length Biases in t-Core Partitions

QEDBENCH: Quantifying the Alignment Gap in Automated Evaluation of University-Level Mathematical Proofs

Hook-Length Biases in t-regular partitions

Arithmetic properties of partition functions introduced by Pushpa and Vasuki

Arithmetic properties of t-Schur overpartitions

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

Symmetric Domino Tilings of Aztec Diamonds

Combinatorial Proofs of Some Results of Andrews and El Bachraoui

Further Arithmetic Properties of Overcubic Partition Triples

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

A Novel Approach to Counting Perfect Matchings of Graphs

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

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 $2^{k}$

Hook Length Biases in $t$ -Core Partitions

Hook-Length Biases in $t$ -regular partitions

Arithmetic properties of $t$ -Schur overpartitions

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