4 papers · 1 filter
Proof of a Conjecture of Cui, Gu and Tang on 18-Colored Generalized Frobenius Partitions
Hirakjyoti Das, Hemjyoti Nath, Abhishek Sarma
Recently, the study of the number of -colored generalized Frobenius partitions, denoted by , has witnessed renewed interest. In this paper, we investigate congruence pr…
Sign Patterns and Congruences of certain infinite products involving the Rogers-Ramanujan continued fraction
Nayandeep Deka Baruah, Abhishek Sarma
We study the behavior of the signs of the coefficients of certain infinite products involving the Rogers-Ramanujan continued fraction. For example, if $$\sum_{n=0}^{\infty}A(n)q^{n…
Congruences and density results for partitions into distinct even parts
Hemjyoti Nath, Abhishek Sarma
In this paper, we consider the set of partitions which counts the number of partitions of wherein the even parts are distinct (and the odd parts are unrestricted). Usi…
Arithmetic properties of -regular partitions into distinct parts
Nayandeep Deka Baruah, Abhishek Sarma
A partition is said to be -regular if none of its parts is a multiple of . Let denote the number of 5-regular partitions into distinct parts (equivalent…