7 papers
Bressoud-Subbarao type weighted partition identities for a generalized divisor function
Archit Agarwal, Subhash Chand Bhoria, Pramod Eyyunni +1
In 1984, Bressoud and Subbarao obtained an interesting weighted partition identity for a generalized divisor function, by means of combinatorial arguments. Recently, the last three…
Generalization of five q-series identities of Ramanujan and unexplored weighted partition identities
Subhash Chand Bhoria, Pramod Eyyunni, Bibekananda Maji
Ramanujan recorded five interesting q-series identities in a section that is not as systematically arranged as the other chapters of his second notebook. These five identities do n…
On the local structure of the set of values of Euler's function
Jean-Marc Deshouillers, Pramod Eyyunni, Sanoli Gun
Assuming the validity of Dickson's conjecture, we show that the set of values of the Euler's totient function contains arbitrarily large arithmetic progressions w…
An inequality between finite analogues of rank and crank moments
Pramod Eyyunni, Bibekananda Maji, Garima Sood
The inequality between rank and crank moments was conjectured and later proved by Garvan himself in 2011. Recently, Dixit and the authors introduced finite analogues of rank and cr…
Combinatorial properties of sparsely totient numbers
Mithun Kumar Das, Pramod Eyyunni, Bhuwanesh Rao Patil
Let and where denotes the Euler's totient function. Masser and Shiu \cite{masser} call th…
Sparse subsets of the natural numbers and Euler's totient function
Mithun Kumar Das, Pramod Eyyunni, Bhuwanesh Rao Patil
In this article, we investigate sparse subsets of the natural numbers and study the sparseness of some sets associated with the Euler's totient function via the property of `Ba…