arXiv subjects

Anjelin Mariya Johnson

Publications and source records attributed to Anjelin Mariya Johnson.

3 recordsLinked to original sources

arXiv2026

Arithmetic Properties for $k$-Color Analogue of Simultaneously $s$-Regular and $t$-Distinct Partitions

In this article, we discuss general generating functions for partitions of $n$, simultaneously $s$-regular and $t$-distinct in 3-colors. In addition, we obtain infinite families of congruences modulo powers of 3 for specific values of $(\ell,t)$. For instance, for positive integers $n$ and $k$, we have \begin{align*} \sum_{n=o}^{\infty}RD_3^{3,3}\left(3^kn+\frac{3^k+1}{2}\right)q^n\equiv0 \pmod{3^{k+1}}. \end{align*}

math.CO↗

arXiv2026

Additional Congruences for generalized Color Partitions of Hirschhorn and Sellers

Let $a_k(n)$ denote the number of partitions of $n$ wherein even parts come in only one color, while the odd parts may be ``colored" with one of $k$ colors, for fixed $k$. In this note, we find some congruences for $a_k(n)$ in the spirit of Ramanujan's congruences. We prove a number of results for $a_k(n)$ modulo powers of $2$ for infinitely many values of $k$. Our approach is truly elementary, relying on generating function manipulations, theta functions and $q$-dissection techniques. We then close by demonstrating an infinite family of congruences modulo 11 which is proven using a result of Ahlgren.

math.NT↗

arXiv2025

On recent Partition function of Kaur and Rana

Recently, Kaur and Rana introduced the partition function denoted by $ρ(n)$, where the largest part $λ$ appears exactly once, and the remaining parts constitute a partition of $λ$. In this paper, we establish new generating functions for certain variants of $ρ(n)$. Further, we obtain a linear recurrence relation for our new generating function.

math.CO↗