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Browsing BITS Faculty Publications by Author "Eyyunni, Pramod"

Browsing BITS Faculty Publications by Author "Eyyunni, Pramod"

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  • Combinatorial properties of sparsely totient numbers 
    Eyyunni, Pramod (ARXIV, 2020)
    Let N1(m) = maxfn: (n) mg and N1 = fN1(m) : m 2 (N)g where (n) denotes the Euler's totient function. Masser and Shiu [3] call the elements of N1 as `sparsely totient num- bers' and initiated the study of these ...
  • Generalization of five q-series identities of Ramanujan and unexplored weighted partition identities 
    Eyyunni, Pramod (Springer, 2022-01)
    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 not seem to have acquired enough attention. ...
  • An inequality between finite analogues of rank and Crank moments 
    Eyyunni, Pramod (ARXIV, 2019-08)
    The inequality between rank and crank moments was conjectured and later proved by Garvan himself in 2011. Recently, Dixit and the authors introduced finite ana- logues of rank and crank moments for vector partitions while ...
  • Minimal excludant over partitions into distinct parts 
    Eyyunni, Pramod (ARXIV, 2022)
    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, studied the concept of the “smallest gap” ...
  • On the local structure of the set of values of Euler's φ function 
    Eyyunni, Pramod (ARXIV, 2021-03)
    Assuming the validity of Dickson's conjecture, we show that the set V of values of the Euler's totient function φ contains arbitrarily large arithmetic progressions with common difference 4. This leads to the question of ...
  • On thin sum-product bases 
    Eyyunni, Pramod (Springer, 2021)
    Additive bases, and less importantly multiplicative bases, have been ex- tensively studied for several centuries. More recently, expanding polynomi- als (of course, with more than one variable) have been considered with ...
  • Sparse subsets of the natural numbers and Euler’s totient function 
    Eyyunni, Pramod (Springer, 2019-08)
    In this article, we investigate sparse subsets of the natural numbers and study the sparseness of some sets associated to the Euler’s totient function φ via the property of ‘Banach density’. These sets related to the ...
  • Untrodden pathways in the theory of the restricted partition function p(n,N) 
    Eyyunni, Pramod (Elsevier, 2021-05)
    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 limiting case gives a finite analogue of ...

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