Author

Gaurab Bardhan

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Preprint Aug 2026

Proofs of the Conjectures on $SOME(n)$ and $DSOME(n)$ Functions Related to Integer Partitions

Andrews and Dastidar (2026) introduced $SOME(n)$ and $DSOME(n)$ functions related to partitions of a positive integer $n$, where $SOME(n)$ is the sum of all the odd parts in the partitions of $n$ minus the sum of all the even parts and $DSOME(n)$ is the sum of all the odd parts in the partitions of $n$ into distinct pa...

Gaurab Bardhan, N. Saikia · 1 citation

Preprint Jul 2026

Analytic proofs of Andrews-Bachraoui identities related to two-color partitions with evens in one color

Andrews and Bachraoui (\textit{Int. J. Number Theory} (2026)) studied the two-color partition function $F(n)$ of a non-negative integer $n$ wherein odd parts may appear in two colors (red and blue) and even parts appear in one color (blue). For any non-negative integer $n,$ they also considered some restricted versions...

Gaurab Bardhan, N. Saikia · 0 citations