A. Singh

activity

20172022

most citedMex-related partitions and relations to ordinary partition and singular overpartitions

2 citations · 2 across the 5 of their papers we have counts for

collaborators

Showing math.NTShow all

6 papers · 1 filter

math.NT2022

Proofs of some conjectures of Keith and Zanello on $t$ -regular partition

Ajit Singh, Rupam Barman

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 famil…

math.NT2021

Proof of some conjectural congruences of da Silva and Sellers

Ajit Singh, Rupam Barman

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…

math.NT2021

Divisibility of certain $ℓ$ -regular partitions by $2$

Ajit Singh, Rupam Barman

For a positive integer $ℓ$ , let $b_{ℓ} (n)$ denote the number of $ℓ$ -regular partitions of a nonnegative integer $n$ . Motivated by some recent conjectures of Keith and Zane…

math.NT2021

Eta-quotients and divisibility of certain partition functions by powers of primes

Ajit Singh, Rupam Barman

Andrews' $(k, i)$ -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 $\equiv \p…

math.NT2020★ 2 cited

Mex-related partitions and relations to ordinary partition and singular overpartitions

Rupam Barman, Ajit Singh

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 familie…

math.NT2020

On Mex-related partition functions of Andrews and Newman

Rupam Barman, Ajit Singh

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-functio…

Proofs of some conjectures of Keith and Zanello on t-regular partition

Proof of some conjectural congruences of da Silva and Sellers

Divisibility of certain ℓ-regular partitions by 2

Eta-quotients and divisibility of certain partition functions by powers of primes

Mex-related partitions and relations to ordinary partition and singular overpartitions

On Mex-related partition functions of Andrews and Newman

Proofs of some conjectures of Keith and Zanello on $t$ -regular partition

Divisibility of certain $ℓ$ -regular partitions by $2$