22 citations · 61 across the 21 of their papers we have counts for
22 papers
Congruences for the Andrews--Uncu partition function
Nayandeep Deka Baruah, Hirakjyoti Das, Manjil P. Saikia +1
In 2018, Andrews defined and studied the partition function , which counts the number of partitions of where each even part is less than each odd part. Thereaf…
Difference of the Sum of All Odd and Even Overlined Parts of Overpartitions
Nayandeep Deka Baruah, Pankaj Gogoi
Recently, Garvan and Sarma studied sums of non-overlined parts in overpartitions and partitions without repeated odd parts. In this paper, we study the corresponding statistic for…
Hook Length Biases in -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…
Arithmetic properties of DSOME function
Nayandeep Deka Baruah, Pankaj Gogoi
Recently, Andrews and Ghosh Dastidar (Ramanujan J. \textbf{69}, Art. No. 26, 2026) studied two interesting functions and , where is the sum of all the…
Combinatorial proofs of some identities on overpartitions with repeated smallest non-overlined part
Nayandeep Deka Baruah, Haijun Li, Pankaj Jyoti Mahanta
Let denote the number of overpartitions of where the smallest non-overlined part, say , appears times and every overlined part is bigger…
Sign Patterns and Congruences of certain infinite products involving the Rogers-Ramanujan continued fraction
Nayandeep Deka Baruah, Abhishek Sarma
We study the behavior of the signs of the coefficients of certain infinite products involving the Rogers-Ramanujan continued fraction. For example, if $$\sum_{n=0}^{\infty}A(n)q^{n…
Arithmetic properties of -regular partitions into distinct parts
Nayandeep Deka Baruah, Abhishek Sarma
A partition is said to be -regular if none of its parts is a multiple of . Let denote the number of 5-regular partitions into distinct parts (equivalent…
Identities for the Rogers-Ramanujan Continued Fraction
Nayandeep Deka Baruah, Pranjal Talukdar
We prove some new modular identities for the Rogers\textendash Ramanujan continued fraction. For example, if denotes the Rogers\textendash Ramanujan continued fraction, then…
Arithmetic Identities for Some Analogs of -core Partition Function
Subhajit Bandyopadhyay, Nayandeep Deka Baruah
Recently, Gireesh, Ray, and Shivashankar studied an analog, , of the -core partition function, . In this paper, we study the function $\overline{a}_5(…
A Note on the Number of Representations of as a Sum of Generalized Polygonal Numbers
Subhajit Bandyopadhyay, Nayandeep Deka Baruah
Recently, Jha (arXiv:2007.04243, arXiv:2011.11038) has found identities that connect certain sums over the divisors of to the number of representations of as a sum of squar…
The -Color Partition Function and Some Counting Theorems
Subhajit Bandyopadhyay, Nayandeep Deka Baruah
Recently, Merca and Schmidt found some decompositions for the partition function in terms of the classical Möbius function as well as Euler's totient. In this paper, we defi…
Congruences for the difference of even and odd number of parts of the cubic and some analogous partition functions
Nayandeep Deka Baruah, Abhishek Sharma
Partitions wherein the even parts appear in two different colours are known as cubic partitions. Recently, Merca introduced and studied the function , which is defined as the…
Witness identities for three Ramanujan congruences
Nayandeep Deka Baruah, Hirakjyoti Das, Abhishek Sarma
For the unrestricted partition function for integers , it is known that , , and $p(49n + 40) \equiv…
Congruences for -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 elongated partition diamonds. Recently, they [2] revisited the topic.…
Matching coefficients in the series expansions of certain -products and their reciprocals
Nayandeep Deka Baruah, Hirakjyoti Das
We show that the series expansions of certain -products have \textit{matching coefficients} with their reciprocals. Several of the results are associated to Ramanujan's continue…
A refinement of a result of Andrews and Newman on the sum of minimal excludants
Nayandeep Deka Baruah, Subhash Chand Bhoria, Pramod Eyyunni +1
In this article, we refine a result of Andrews and Newman, that is, the sum of minimal excludants over all the partitions of a number equals the number of partitions of int…
Families of Congruences for Fractional Partition Functions Modulo Powers of Primes
Nayandeep Deka Baruah, Hirakjyoti Das
Recently, Chan and Wang (Fractional powers of the generating function for the partition function. Acta Arith. 187(1), 59--80 (2019)) studied the fractional powers of the generating…
Results on some partition functions arising from certain relations involving the Rogers-Ramanujan continued fractions
Nayandeep Deka Baruah, Nilufar Mana Begum, Hirakjyoti Das
Relations involving the Rogers-Ramanujan continued fractions and are used to find new generating functions and congruences modulo 5 and 25 for 3-core, 4…
Generating Functions and Congruences for Some Partition Functions Related to Mock Theta Functions
Nayandeep Deka Baruah, Nilufar Mana Begum
Recently, Andrews, Dixit and Yee introduced partition functions associated with Ramanujan/Watson third order mock theta functions and . In this paper, we find several…
Some results on vanishing coefficients in infinite product expansions
Nayandeep Deka Baruah, Mandeep Kaur
Recently, M. D. Hirschhorn proved that, if and $\sum_{n=0}^\infty b_nq^n:=(-q^2,-q^3;q^5)_\infty(q^3,q^7;q…
Proofs of Some Conjectures of Chan on Appell-Lerch Sums
Nayandeep Deka Baruah, Nilufar Mana Begum
On page 3 of his lost notebook, Ramanujan defines the Appell-Lerch sum which is connected to some of his si…
New Congruences Modulo 2, 4, and 8 for the Number of Tagged Parts Over the Partitions with Designated Summands
Nayandeep Deka Baruah, Mandeep Kaur
Recently, Lin introduced two new partition functions PD and PDO, which count the total number of tagged parts over all partitions of with designated summands and…