7 citations · 11 across the 14 of their papers we have counts for
15 papers
Elementary symmetric polynomials and a potentially injective family of maps on partitions
Aman Devnani, Pramod Eyyunni
In this article, we provide an infinite family of examples to disprove a recent conjecture due to Ballantine and her collaborators on the injectivity of a class of maps, namely pre…
On the number of missing integers in partitions
Subhash Chand Bhoria, Pramod Eyyunni, Subhrangsu Santra
In the preceding decade, Andrews and Newman resurrected the concept of a `minimal excludant' of a partition (, for short), namely, the least positive missing integer in a part…
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…
On the combinatorics of r-chain minimal and maximal excludants
Subhash Chand Bhoria, Pramod Eyyunni, Runqiao Li
The minimal excludant (mex) of a partition was introduced by Grabner and Knopfmacher under the name `least gap' and was revived by a couple of papers due to Andrews and Newman. It…
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…
A new generalization of the minimal excludant arising from an analogue of Franklin's identity
Subhash Chand Bhoria, Pramod Eyyunni, Bibekananda Maji
Euler's classical identity states that the number of partitions of an integer into odd parts and distinct parts are equinumerous. Franklin gave a generalization by considering part…
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…