7 citations · 11 across the 14 of their papers we have counts for
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A divisor generating -series and cumulants arising from random graphs
Archit Agarwal, Subhash Chand Bhoria, Pramod Eyyunni +2
Uchimura, in 1987, introduced a probability generating function for a random variable and using properties of this function he discovered an interesting -series identity. He…
A divisor generating q-series identity and its applications to probability theory and random graphs
Archit Agarwal, Subhash Chand Bhoria, Pramod Eyyunni +1
In I981, Uchimura studied a divisor generating -series that has applications in probability theory and in the analysis of data structures, called heaps. Mainly, he proved the fo…
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…
Minimal excludant over partitions into distinct parts
Prabh Simrat Kaur, Subhash Chand Bhoria, Pramod Eyyunni +1
The average size of the "smallest gap" of a partition was studied by Grabner and Knopfmacher in 2006. Recently, Andrews and Newman, motivated by the work of Fraenkel and Peled, stu…
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…
Untrodden pathways in the theory of the restricted partition function
Atul Dixit, Pramod Eyyunni, Bibekananda Maji +1
We obtain a finite analogue of a recent generalization of an identity in Ramanujan's Notebooks. Differentiating it with respect to one of the parameters leads to a result whose lim…