Gaurab Bardhan

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math.NT2026

Proofs of the Conjectures on $S O M E (n)$ and $D S O M E (n)$ Functions Related to Integer Partitions

Gaurab Bardhan, Nipen Saikia

Andrews and Dastidar (2026) introduced $S O M E (n)$ and $D S O M E (n)$ functions related to partitions of a positive integer $n$ , where $S O M E (n)$ is the sum of all the odd parts in the pa…

math.NT2026

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

Gaurab Bardhan, Nipen Saikia

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 colo…

math.NT2026

Some new congruences and identities for $S O M E (n)$ , $D S O M E (n)$ , $S O M E (n)$ functions and analogues

Gaurab Bardhan, Nipen Saikia

Andrews and Dastidar (\textit{Ramanujan J. 69, Article Number 26, (2026)} ) introduced the $S O M E (n)$ and $D S O M E (n)$ functions that calculate the sum of all odd parts minus the sum…

math.NT2026

Relations for partitions with distinct even parts except the largest part which is even

Gaurab Bardhan, Nipen Saikia

In this paper, we prove some new $q$-series identities connecting $4$-regular partitions and partitions with distinct even parts with largest part being odd. We also define thr…

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

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

Some new congruences and identities for SOME(n), DSOME(n), SOME(n) functions and analogues

Relations for partitions with distinct even parts except the largest part which is even

Proofs of the Conjectures on $S O M E (n)$ and $D S O M E (n)$ Functions Related to Integer Partitions

Some new congruences and identities for $S O M E (n)$ , $D S O M E (n)$ , $S O M E (n)$ functions and analogues