Author

Manjil P. Saikia

Cardiff University

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Preprint Sep 2026

Congruences for the Andrews--Uncu partition function $\mathcal{EO}_u(n)$

In 2018, Andrews defined and studied the partition function $\mathcal{EO}(n)$, which counts the number of partitions of $n$ where each even part is less than each odd part. Thereafter, Uncu considered a different subset of such partitions, namely those partitions counted by $\mathcal{EO}(n)$ where there are no repeated...

Nayandeep Deka Baruah, Hirakjyoti Das, Manjil P. Saikia et al. · 0 citations

Preprint Sep 2026

On the positivity of truncated pentagonal number series and some conjectures of Merca

Let $\nu_2(m)$ denote the $2$-adic valuation of a positive integer $m$ and set $N_m=m\bigl(1+\nu_2(m)/2\bigr)$. We prove four conjectures of Merca on the nonnegativity of truncated pentagonal number series weighted by the infinite products $\prod_{m\ge 1}(1-q^{2N_m})$ and $\prod_{r\ge 1}\bigl(q^{2^r r};q^{2^{r+1}r}\big...

Manjil P. Saikia, Abhishek Sarma · 0 citations

Preprint Sep 2026

Generalized Frobenius Partitions Modulo Powers of $2$

Let $c\phi_k(n)$ denote the number of $k$-colored generalized Frobenius partitions of $n$. We prove that, for every $m\geq2$ and every $k\equiv2\pmod{2^m}$, \[ \sum_{n\geq0}c\phi_k(n)q^n\equiv\frac{\varphi(q)\,(q^2;q^2)_\infty}{(q;q)_\infty^2}\sum_{n\geq0}c\phi_{k/2}(n)q^{2n}\pmod{2^m}, \] where $\varphi(q)$ is the cla...

Manjil P. Saikia · 0 citations