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Suparno Ghoshal

Publications and source records attributed to Suparno Ghoshal.

5 recordsLinked to original sources
arXiv2026

Proof of a Conjecture on Overcolored Partition Restricted by Parity of the Parts

In a recent paper, Thejitha and Fathima introduced the overcolored partition function $\bar{a}_{r,s}(n)$, which enumerates overpartitions in which even parts may appear in one of $r$ colors and odd parts in one of $s$ colors, for fixed integers $r,s \geq 1$. They also proposed several conjectures concerning families of congruences modulo powers of $2$ for specific arithmetic progressions of $\bar{a}_{r,s}(n)$. In this paper, we provide an elementary proof of this conjecture that relies only on classical $q$-series manipulations and properties of Ramanujan's theta function.

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arXiv2025

Further results on arithmetic properties of biregular overpartitions

Recently there has been quite a bit of study carried out related to arithmetic properties of overpartitions into non-multiples of two co-prime integers. The paper [19] by Nadji et al. looked into congruences modulo $3$ and powers of $2$ for certain specific pairs of co-prime integers, while the paper [1] by Alanazi et al. investigated some congruences related to some similar and some different pairs of co-prime integers. In this paper we propose some elegant and elementary proofs of a subset of the congruences given in [1] by using only theta function and dissection identities. We also propose a generic method for proving congruences modulo $8$ which doesn't necessarily use any specific $2$-dissection.

math.NT↗
arXiv2025

Discussion on some conjectures regarding the periodicity of sign patterns of certain infinite products involving the Rogers-Ramanujan Continued Fractions

Let $R(q)$ denote the Rogers-Ramanujan continued fraction. Define $$ \frac{1}{R^5(q)}=\displaystyle \sum_{n=0}^{\infty}A(n)q^{n} \quad \text{and} \quad R^5(q)=\displaystyle\sum_{n=0}^{\infty}B(n)q^{n}.$$ Baruah and Sarma recently posed conjectures regarding the sign patterns of $A(5n), B(5n)$ for $n\geq 0.$ In this paper, we show that these conjectures do not hold for $n=0$.

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arXiv2018

Some Observations on Modulo 5 Congruences for 2-Color Partitions

The 2-color partitions may be considered as an extension of regular partitions of a natural number $n$, with $p_{k}(n)$ defined as the number of 2-colored partitions of $n$ where one of the 2 colors appears only in parts that are multiples of $k$. In this paper, we record the complete characterization of the modulo 5 congruence relation $p_{k}(25n + 24 - k) \equiv 0 \pmod{5}$ for $k \in \{1, 2, \ldots, 24\}$, in connection with the 2-color partition function $p_k(n)$, providing references to existing results for $k \in \{1, 2, 3, 4, 7, 8, 17\}$, simple proofs for $k \in \{5, 10, 15, 20\}$ for the sake of completeness, and counter-examples in all the remaining cases. We also propose an alternative proof in the case of $k = 4$, without using the Rogers-Ramanujan ratio, thereby making the proof considerably simpler compared to the proof by Ahmed, Baruah and Ghosh Dastidar (JNT 2015).

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