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math.NT2026
Untrodden pathways in the study of partitions with parts separated by parity
Nargish Punia, Rahul Kumar
In this paper, we study a partition function with parts separated by parity from a family of partition functions introduced by Andrews in 2019. We first show that its generating fu…
math.OA2026
Irreducibility and weak spectral gap in free product von Neumann algebras
Aldo Garcia Guinto, Fehmi Ekin Giritlioglu, Rahul Kumar R. +2
Consider a free product of non-trivial von Neumann algebras. Using amalgamated free product techniques, we establish irreducibility and weak spectral…
math.CO2026
On Partition Classes Arising from Parity, Differences, and Repeated Smallest Parts
Rahul Kumar, Nargish Punia
In this paper, we study various classes of partition functions such as those related to the parity of the number of parts, to differences of partition numbers, and to partitions wi…