Journal of the Ramanujan Mathematical Society
Volume 39, Issue 4, December 2024 pp. 349–358.
Extensions of some results of Jovovic and Dhar
Authors:
Pankaj Jyoti Mahanta and Manjil P. Saikia
Author institution:Gonit Sora, Dhalpur, Assam 784 165, India
Summary:
We look at extensions of formulas given by Jovovic and recently proved by Dhar on integer partitions
where the smallest part occurs at least m times and on integer partitions with fixed differences between the largest
and smallest parts where the smallest part occurs at least k times. Our results extend Dhar’s results for the m = 2
and k = 1 cases to the general cases for arbitrary m and k. We also look at analogous results for overpartitions and
ℓ-regular partitions.
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