10 papers
Arithmetic properties of DSOME function
Nayandeep Deka Baruah, Pankaj Gogoi
Recently, Andrews and Ghosh Dastidar (Ramanujan J. \textbf{69}, Art. No. 26, 2026) studied two interesting functions and , where is the sum of all the…
Hook Length Biases in -Core Partitions
Nayandeep Deka Baruah, Hirakjyoti Das, Pankaj Jyoti Mahanta +1
Recently, the theory of hook length biases has emerged as a prominent research topic. Led by Ballantine, Burson, Craig, Folsom, and Wen [\textit{Res. Math. Sci.}, 2023], hook lengt…
Combinatorial proofs of some identities on overpartitions with repeated smallest non-overlined part
Nayandeep Deka Baruah, Haijun Li, Pankaj Jyoti Mahanta
Let denote the number of overpartitions of where the smallest non-overlined part, say , appears times and every overlined part is bigge…
A refinement of a result of Andrews and Newman on the sum of minimal excludants
Nayandeep Deka Baruah, Subhash Chand Bhoria, Pramod Eyyunni +1
In this article, we refine a result of Andrews and Newman, that is, the sum of minimal excludants over all the partitions of a number equals the number of partitions of int…
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…
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…