10 papers
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…
Some new results for Andrews' Kimberling partitions
Gaurab Bardhan, Nipen Saikia
George E. Andrews (2016) introduced the Kimberling index, , of a partition of a positive integer , which is defined as $$K(π) = (\text{largest part of } π) - (\text{le…
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…
Integer Partitions With Restricted Distinct Parts
Rinchin Drema, Nipen Saikia
For any positive integers and , let denotes the number of partitions of a positive integer into distinct parts such that no part is congruent to or $t…