5 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 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…
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…