Ajit Singh

Ajit Singh
Indian Institute of Technology Guwahati | IIT Guwahati · Department of Mathematics

Doctor of Philosophy

About

15
Publications
742
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12
Citations
Citations since 2017
15 Research Items
12 Citations
201720182019202020212022202302468
201720182019202020212022202302468
201720182019202020212022202302468
201720182019202020212022202302468
Introduction
Skills and Expertise

Publications

Publications (15)
Preprint
For a positive integer $t\geq 2$, let $b_{t}(n)$ denote the number of $t$-regular partitions of a nonnegative integer $n$. In a recent paper, Keith and Zanello investigated the parity of $b_{t}(n)$ when $t\leq 28$. They discovered new infinite families of Ramanujan type congruences modulo 2 for $b_{21}(n)$ involving every prime $p$ with $p\equiv 13...
Preprint
For a positive integer $t\geq 2$, let $b_{t}(n)$ denote the number of $t$-regular partitions of a nonnegative integer $n$. Motivated by some recent conjectures of Keith and Zanello, we establish infinite families of congruences modulo $2$ for $b_9(n)$ and $b_{19}(n)$. We prove some specific cases of two conjectures of Keith and Zanello on self-simi...
Article
Full-text available
For a positive integer \(\ell \), let \(b_{\ell }(n)\) denote the number of \(\ell \)-regular partitions of a nonnegative integer n. Motivated by some recent conjectures of Keith and Zanello, we establish infinite families of congruences modulo 2 for \(b_3(n)\) and \(b_{21}(n)\). We prove a specific case of a conjecture of Keith and Zanello on self...
Preprint
For a positive integer $t$, let $b_{t}(n)$ denote the number of $t$-regular partitions of a nonnegative integer $n$. In a recent paper, Keith and Zanello established infinite families of congruences and self-similarity results modulo $2$ for $b_{t}(n)$ for certain values of $t$. Further, they proposed some conjectures on self-similarities of $b_t(n...
Article
Let $p_{\{3, 3\}}(n)$ denote the number of $3$ -regular partitions in three colours. Da Silva and Sellers [‘Arithmetic properties of 3-regular partitions in three colours’, Bull. Aust. Math. Soc. 104 (3) (2021), 415–423] conjectured four Ramanujan-like congruences modulo $5$ satisfied by $p_{\{3, 3\}}(n)$ . We confirm these conjectural congruences...
Preprint
For a positive integer $\ell$, let $b_{\ell}(n)$ denote the number of $\ell$-regular partitions of a nonnegative integer $n$. Motivated by some recent conjectures of Keith and Zanello, we establish infinite families of congruences modulo $2$ for $b_3(n)$ and $b_{21}(n)$. We prove a specific case of a conjecture of Keith and Zanello on self-similari...
Preprint
Let $p_{\{3, 3\}}(n)$ denote the number of $3$-regular partitions in three colours. In a very recent paper, da Silva and Sellers studied certain arithmetic properties of $p_{\{3, 3\}}(n)$. They further conjectured four Ramanujan-like congruences modulo $5$ satisfied by $p_{\{3, 3\}}(n)$. In this article, we confirm the conjectural congruences of da...
Article
Full-text available
The minimal excludant, or “mex” function, on a set S of positive integers is the least positive integer not in S. In a recent paper, Andrews and Newman extended the mex-function to integer partitions and found numerous surprising partition identities connected with these functions. Very recently, da Silva and Sellers present parity considerations o...
Article
Full-text available
Andrews introduced the singular overpartition function C‾k,i(n) which counts the number of overpartitions of n in which no part is divisible by k and only parts ≡±i(modk) may be overlined. In this article, we study the divisibility properties of C‾4k,k(n) and C‾6k,k(n) by arbitrary powers of 2 and 3 for infinite families of k. For an infinite famil...
Article
In a recent paper, Andrews and Newman introduced certain families of partition functions using the minimal excludant or "mex" function. In this article, we study two of the families of functions Andrews and Newman introduced, namely p t,t (n) and p 2t,t (n). We establish identities connecting the ordinary partition function p(n) to p t,t (n) and p...
Article
Andrews introduced the partition function $\overline {C}_{k, i}(n)$ , called the singular overpartition function, which counts the number of overpartitions of n in which no part is divisible by k and only parts $\equiv \pm i\pmod {k}$ may be overlined. We prove that $\overline {C}_{6, 2}(n)$ is almost always divisible by $2^k$ for any positive inte...
Preprint
Andrews' $(k, i)$-singular overpartition function $\overline{C}_{k, i}(n)$ counts the number of overpartitions of $n$ in which no part is divisible by $k$ and only parts $\equiv \pm i\pmod{k}$ may be overlined. In recent times, divisibility of $\overline{C}_{3\ell, \ell}(n)$, $\overline{C}_{4\ell, \ell}(n)$ and $\overline{C}_{6\ell, \ell}(n)$ by $2...
Article
Full-text available
In order to give overpartition analogues of Rogers-Ramanujan type theorems for the ordinary partition function, Andrews defined the so-called singular overpartitions. Singular overpartition function C‾k,i(n) counts the number of overpartitions of n in which no part is divisible by k and only parts ≡±i(modk) may be overlined. Andrews also proved two...
Preprint
The minimal excludant, or "mex" function, on a set $S$ of positive integers is the least positive integer not in $S$. In a recent paper, Andrews and Newman extended the mex-function to integer partitions and found numerous surprising partition identities connected with these functions. Very recently, da Silva and Sellers present parity consideratio...
Preprint
In a recent paper, Andrews and Newman introduced certain families of partition functions using the minimal excludant or "mex" function. In this article, we study two of the families of functions Andrews and Newman introduced, namely $p_{t,t}(n)$ and $p_{2t,t}(n)$. We establish identities connecting the ordinary partition function $p(n)$ to $p_{t,t}...

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