6 papers · 1 filter
Divisibility Properties of Odd Part and Even Part Sums in Cubic Partitions
Gaurab Bardhan, Nipen Saikia
A cubic partition of a positive integer is a partition of in which even parts may appear in two distinct colors. The purpose of this paper is to study the arithmetic functi…
On partitions with bounded multiplicity restrictions on even parts and with the largest part being odd
Gaurab Bardhan, Nipen Saikia
Andrews and El Bachraoui (\textit{RACSAM} \textbf{119}, \textit{Article Number 4 (2025)}) established identities relating -regular partitions to partitions with distinct even pa…
Proofs of the Conjectures on and Functions Related to Integer Partitions
Gaurab Bardhan, Nipen Saikia
Andrews and Dastidar (2026) introduced and functions related to partitions of a positive integer , where is the sum of all the odd parts in the pa…
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 of a non-negative integer wherein odd parts may appear in two colo…
Some new congruences and identities for , , functions and analogues
Gaurab Bardhan, Nipen Saikia
Andrews and Dastidar (\textit{Ramanujan J. 69, Article Number 26, (2026)} ) introduced the and functions that calculate the sum of all odd parts minus the sum…
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…